# The parabola y2 = 4ax, where a > 0, and the rectangular hyperbola xy = C2, where C > 0, intersect at right angles. Show that the tangent and normal to either curve at the point of intersection meet the

6,496 results
1. ## Math

a rectangular object 25 m wide is to pass under a parabolic arc that has width of 32m at the base and a height 24m at the center. If the vertex of the parabola is at the top ofbthe arch, what maximum height should the rectangular object have?

2. ## Calculus

Find expressions for the quadratic functions whose graphs are shown. One graph has the point (4,2) plotted in which the parabola passes through (U-shaped parabola- right side up) The vertex is at (3,0) and the parabola does not touch the y-axis for as much

3. ## pre cal

What is the center of the conic whose equation is x^2 + 2y^2 - 6x + 8y = 0 2.Which one of the following equations represents a hyperbola? (5 points) A) 3x^2 + y^2 + 12x - 7 = 0 B) 3x^2 + 3y^2 + 12x - 7 = 0 C) 3x^2 + y + 12x - 7 = 0 D) 3x^2 - 3y^2 + 12x - 7

4. ## Calculus

a hyperbola passing through (8,6) consists of all points whose distance from the origin is a constant more than its distance from the point (5,2). find the slope of the tangent line to the hyperbola at (8,6).

5. ## further math

identify the conic sections below (circle,hyperbola,parabola,ellipse). a)3x2+3y2-2y=4 b)3x2-9y2+2x-4y=7 c)2x2+5y2-7x+3y-4=0 d)3y2-4x+17y=-10

6. ## Algebra

The reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 60 inches wide and 30 inches deep, how far from the vertex should the microphone

7. ## Algebra 2

A hyperbolic mirror can be used to take panoramic photos, if the camera is pointed toward the mirror with the lens at one focus of the hyperbola. Write the equation of the hyperbola that can be used to model a mirror that has a vertex 4 inches from the

8. ## Algebra

The vertex of a parabola represented by f(x)=x^2-4x+3 has coordinates of (2,-1). Find the coordinates of the vertex of the parabola defined by g(x)=f(x-2). Explain how you arrived to your answer. My question: Would you move the parabola represented by f(x)

9. ## Math

1.) If a = 2 and the vertex of a parabola is (3, -4), will there be a minimum or maximum value for the parabola? What is the value? 2.) If a = 2 and the vertex of a parabola is (3, -4), what is its axis of symmetry?

10. ## Parabola Ques

Find the point P on the parabola y^2 = 4ax such that area bounded by parabola, the X-axis and the tangent at P is equal to that of bounded by the parabola, the X-axis and the normal at P.

11. ## Math Word Problem

A cross section of a nuclear cooling tower is a hyperbola with equation x^2/90^2-y^2/130^2=1. The tower is 450ft tall and the distance from the top of the tower to the center of the hyperbola is half the distance from the base of the tower to the center of

12. ## math

An ellipse and a hyperbola have the same foci, \$A\$ and \$B\$, and intersect at four points. The ellipse has major axis 50, and minor axis 40. The hyperbola has conjugate axis of length 20. Let \$P\$ be a point on both the hyperbola and ellipse. What is \$PA

13. ## algebra

6. Find the equation of each parabola described below. a) parabola with vertex (0,0) and the focus (0,7) b) parabola with focus (-3,0) and directrix x=3 c) parabola with vertex (3,3) and directrix x=-1 d) parabola with focus (-2,-1) and directrix y=5 e)

14. ## Calculus

Find the length of the parabola y^2=4ax cut off the line x=a about the x-axis

15. ## Physics

According to Boyles' law, PV = constant. If a graph is plotted with the pressure P against the volumeV, the graph would be a a.straight line b.parabola c.hyperbola d.ellipse

16. ## physics

During an experiment that Paul and Dawn performed the stretch of a spring was directly proportional to the force applied to the spring. When they put the data on a graph, they would expect to have what type of curve? Answers: Hyperbola, parabola, straight

17. ## algebra

HYPERBOLA Q!! Find an equation for a horizontal hyperbola with vertices that are 20 units apart from each other and foci 30 units apart each other?? im lost on this any help is appreciated !!!

18. ## Math

Please Check My Answers!!! What is the type of conic section is given by the equation x^2-9y^2=900 and what is the domain and range? Answer: Type is hyperbola, Domain is all real values of x, not sure what the range is. Please explain how to find these

19. ## math

A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) The parabola has a minimum value B) The parabola has a maximum value C) The parabola does not cross the y-axis D) The parabola does not cross the x-axis E) The vertex of the parabola

20. ## algebra

a hyperbola has vertices (+-5,0) and one focus (6,0) what is the standard form equation of the hyperbola.

21. ## analytic geometry

Find the equation of the hyperbola. Transverse axis parallel to the x-axis, center at (5,1), the rectangle on the axes of the hyperbola of area 48 and distance betwern foci 10. i do nt know how . sorry . pls do help me ..

22. ## algebra

4ax+8a-10x-20

23. ## algebra 2

Determine values for A, B, and C such that the equation below represents the given type of conic. Each axis of the ellipse, parabola, and hyperbola should be horizontal or vertical. Then rewrite your equation for each conic in standard form, identify (h,

24. ## Conics

What type of conic is represented by the polar equation? r= 1 / 4-6cos theta Ellipse Hyperbola Parabola Circle Help! Homework help needed

25. ## precalculus

use the discriminant to determine whether the equation is a parabola, an ellipse, or a hyperbola. Then identify the angle of rotation required to eliminate the xy-term. x^2+4xy+y^2=1 5x^2-6xy+5y^2-8x+8y-8=0 9x^2+24xy+16y^2=25

26. ## Algebra 2

The graph of 5x - 9y^2 = 12 - 4y is the graph of a(n)______. a. circle b. ellipse c. hyperbola d. parabola C?

27. ## Math

14) Consider the parabola with equation y = x^2 - 6x + 5. a. Use any suitable method to determine the coordinates of the turning point of this parabola. b. Hence, state for which values of c the line y = c will intersect the parabola: i. twice ii. once

28. ## MATH

a. Write an equation compared to the equation of the standard parabola that satisfies the description of each parabola. 1. A parabola whose vertex is (0, -3) 2. A parabola whose vertex is (5, 1) 3. A parabola that opens down and is compressed vertically by

29. ## Algebra: Parabolas

I have a math problem that requires me to find the focal length of a parabola using the information given on a graph. It is a standard horizontal parabola, the formula being y^2 = ax. The focus point is formula a = 4p. I know that a is positive, because

30. ## Calc I

Find the range of y = (3x-1)/(2x^2 + x - 6) I was going to take the derivative of the numerator and denomenator and then use the quotent rule to find the derivative of the function and find the critical values but I ran into the imaginary number during the

31. ## math

Classify the conic section as a circle, an ellipse, a hyperbola, or a parabola. 25x2=64+16y ellipse parabola circle hyperbola

32. ## Paarabola Ques

what is the conditon fost. line y=mx+c to be normal to parabola y^2=4ax?

33. ## Algebra II

I am lost on this one!!! Determine values for A, B, and C such that the equation below represents the given type of conic. Each axis of the ellipse, parabola, and hyperbola should be horizontal or vertical. Then rewrite your equation for each conic in

34. ## Algebra II

x^2 -12y = 12x -12 is a graph of a(n) a) Ellipse b) circle c) parabola d) hyperbola

35. ## trigonometry

classify the graph of the equation -4y^2+5X+3y+7=0 as a circle, a parabola, an ellipse, or a hyperbola.

36. ## geometry

I need images of Conic Sections: circle, ellipse, hyperbola and parabola...(those larger ones)...

37. ## Pre-Calculus Help?

What conic section is drawn by the parametric equations x=csc t and y cot? A. Parabola B. Circle C. Ellipse D. Hyperbola

38. ## Mathematics

The difference between the x-coordinates of two points on the parabola y^2=4ax is fixed at 2k. Find the equation that describes the position(xp, py)of the point of intersection P of the tangents at the two points. The equation is in the form yp^2=f(xp).

39. ## Geometry

Let A and B be two points on the hyperbola xy=1, and let C be the reflection of B through the origin. (a) Show that C is on the hyperbola. (b) Let Γ be the circumcircle of triangle ABC and let A' be the point on Γ diametrically opposite A. Show that A'

40. ## Algebra II

In this set of eight problems, we have to match each equation with the correct description of its graph. However, these are test corrections I'm doing and I do not have the previous multiple choice answers so I can deduct from it, but can someone help me?

41. ## MathLog#4

A degenerate cone results when the intersectoin of a plane with a double napped con is not a parabola, circle, elllipse, or hyperbola. When a plane parallel to the cone's nappe passes through the cone ,it can creat parabola. What can also be created when a

42. ## Algebra

HELP! I am not sure how I would even start this problem or solve it. A hyperbola with a horizontal transverse axis contains the point at (4, 3). The equations of the asymptotes are y-x=1 and y+x=5 Write an equation for the hyperbola.

43. ## Parabola Help

by plotting the graph of parabola y=2+3x-2x^2 which 3 option are true 1) the graph is the same as that of y=6+9x-6x^2 2)the parabola has a minimum point 3)the gradient of the parabola at x=2 is 0 4)the graphy=2+3x-2x^2crosses the x-axis at the same point

44. ## Algebra

The directrix of a parabola is y=9 . The focus of the parabola is (2,5) . What is the equation of the parabola? y=−1/8(x−2)^2+7 y=1/8(x−2)^2−7 y=1/8(x−2)^2+7 y=−1/8(x−2)^2−7

45. ## agebra

Can someone please help me.. find an equation that models the path of a satelite if its path is a hyperbola, a=55,000km and c=81,000km assume that the center of the hyperbola is the origin and the tranverse axis is horizontal

46. ## math

what's the quadratic form of 1/4(x+3)^2-4 I need it to find the intercepts of the parabola it describes. Check: I think the parabola is 1/4 scaled, moved 3 to the left and down 4 compared to a y=x^2 parabola. Is this ok? If you are looking for the

47. ## algebra

A parabolic microphone has a cross-section in the shape of a parabola. The microphone is placed at the focus of the parabola. If the parabola is 20 inches wide and 5 inches deep, how far from the vertex should the microphone be placed? Can someone please

48. ## Algebra 2

Can someone check my answers? 1. Convert 13pi/30 to degree measure. 78° 2. Find the distance between (4,4) and (8,7). 5 3. What is the vertex of the parabola y = (x + 8)^2 - 2? (-8,-2) 4. The graph of y = 6(x - 8)^2 + 1 open downward. False. 5. An angle

49. ## Math, Related Rates

Consider the hyperbola y = 1/x and think of it as a slide. A particle slides along the hyperbola so that its x-coordinate is increasing at a rate of f(x) units/sec. If its y-coordinate is decreasing at a constant rate of 1 unit/sec, what is f(x)? -I

50. ## maths

The parabola y2 = 4ax, where a > 0, and the rectangular hyperbola xy = C2, where C > 0, intersect at right angles. Show that the tangent and normal to either curve at the point of intersection meet the x-axis at T and N where TN = 2pa, where p is an

51. ## Parabola/Hyperbola

Not really for homework help, but just for curiousity. Is there a way to distinguish whether the graph is a parabola or a hyperbola if you do not know the equations and one side of the hyperbola is missing (so there's just one U shape) by restricting the

52. ## Precalculus(URGENT)

write the parabola in y squared=4ax or x squared =4ax form where x equals the distance between the foci and the centerpoint y= -(x+3)squared +4 i have no idea how to do this can you tell me how you got the solution

53. ## maths

Q.1 PQ RS are the two perpendicular chords of the rectangular hyperbola xy = c^2.If C is the center of the rectangular hyperbola,then the product of the slopes of CP,CQ,CR&CSis equal to______ Q.2If PN is the perpendicular from a point P on the rectangular

54. ## math

An equitorial triangles is inscribed in the parabola y^2=4ax, where one vertex is vertex of parabola. what will be the length of the side of triangle?

55. ## math

what are the general equations for the conic sections 1)parabola 2)circle 3)ellipse 4)hyperbola 5)inverse hyperbola

56. ## algebra 2

Determine values for A, B, and C such that the equation below represents the given type of conic. Each axis of the ellipse, parabola, and hyperbola should be horizontal or vertical. Then rewrite your equation for each conic in standard form, identify (h,

57. ## maths

A variable tangent to the ellipse (x/a)^2 +(y/b)^2 meets the parabola y^2=4ax at L and M. Find the locus of the midpoint of LM.

58. ## maths

A Variable Tangent To The Ellipse (x/a)^2 + (y/b)^2 =1 meets the parabola y^2=4ax at L and M. Find the locus of the midpoint of L M

59. ## maths parabola

In a parabola y²=4ax, the length of the chord passing through the vertex & inclined to the x-axis @ an angle π/6 (pi/6) is? Step plz

60. ## math30

The equation of the hyperbola is (x-3)^2/4 - (y+1)^2/16 =-1. What is the range? All I know is this but I am not even sure what I am doing!! My answer: The general form of the equation of a horizontally aligned hyperbola is: (x-h)^2/a^2 - (y-k)^2/b^2 =1. So

61. ## algebra

1)What is the 4x^2=y^2+8y+32 answer= either hyperbola or parabola 2)The graph of which equation is a circle? answer= 5x^2+10x+5y=9 3)Solve the system of equations by graphing x^2+y^2=16 and y= -x+4 answer= (4,0),(0,-4) 4)Find the exact solutions of each

62. ## precalculus

Given: r = 4/-2-costheta What type of conic does this represent? ________________________________________ Circle Ellipse Hyperbola Parabola

63. ## pre-calculus

How do i know if a conic section is a circle, ellipse, hyperbola, or parabola? based on it's equation such as 4x^2 - y^2 + 24x + 4y + 28 = 0

64. ## Math

Classify the conic section 4x^2+5y^2-16x-30y+41=0 as a circle, ellipse, hyperbola, or parabola?

65. ## precalculus

Given: r = 4/-2-6sintheta What type of conic does this represent? ________________________________________ Circle Ellipse Hyperbola Parabola

66. ## algebra help please

I notice that other problems are answered in a timely manner....was is my overlooked? Determine values for A, B, and C such that the equation below represents the given type of conic. Each axis of the ellipse, parabola, and hyperbola should be horizontal

67. ## Parabola ques

the normal to a parabola y^2=4ax at the point t,where t is not 0 meets the curve again at the point t'.find t' in terms of t.determine a point on the x-axis where the tangent at t' meets the x-axis.

68. ## math

A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) The parabola has a minimum value B) The parabola has a maximum value C) The parabola does not cross the y-axis D) The parabola does not cross the x-axis E) The vertex of the parabola

69. ## Algebra 2

The graph of 11x - x^2 - 4y^2 = 2y - 16 is the graph of a(n) ________. a. circle b. ellipse c. hyperbola d. parabola C?

70. ## calculus plz help me

Show that the numerical value of the radius of curvature at the point (x1, y1) on the parabola y^2=4ax is [2(a+x1)^3/2)]/a^1/2. If c is the centre of the curvature at the origin O and S is the point (a, 0), show that OC=2(OS) plz show me working plz

71. ## algebra

Please help with this problem: An ellipse and a hyperbola have the same foci, \$A\$ and \$B\$, and intersect at four points. The ellipse has major axis 50, and minor axis 40. The hyperbola has conjugate axis of length 20. Let \$P\$ be a point on both the

72. ## chuka university

given the eccentilisty and a point that lies on the hyperbola ,find the equation of the hyperbola center origin

73. ## Algebra 2

a hyperbola is centered at (3,7). The vertices are (9,7) and (-3,7). The slopes of the aymptotes are m==/-5/6. Enter the equation of the hyperbola in the form: (x-h)^2/a^2-(y-k)^2/b^2=1

74. ## maths

a hyperbola of eccentricity 3/2 has one focus at (1,-3). The corresponding directrix is the line "y". find an equation for the hyperbola?

75. ## algebra

Can someone please help... a hyperbola has vertices (+-5,0) and one focus (6,0) what is the standard form equation of the hyperbola.

76. ## Math

Write the equation of the hyperbola with the following info: The hyperbola has vertices (–2, 9) and (–2, 3) and foci (–2, 13) and (–2, –1);

77. ## MATH!+ check please~ thanks in advance!

the equation 2x^2+ cy^2+Dx+Ey+f= 0 represent a conic. state the value(s) of C for which each of the following are possible: A circle: My answer: c= 2 an ellipse: My answer: c>0, cant equal 2 Parabola: My answer:c=0 a hyperbola: My answer: c

78. ## Algebra

I'm trying this again, I'd like the quadratic form, so i can then work the intercepts myself. SO: what's the quadratic form of 1/4(x+3)^2-4 I need it to find the intercepts of the parabola it describes. Check: I think the parabola is 1/4 scaled, moved 3 to

79. ## Algebra II-Please check fpr explanation

I have a question concerning this problem:I just want to make sure my formulas are correct before I do problem It is a hyperbola equation (y-4)^2/49 - (x-6)^2/72 = 1 1.It is a vertical hyperbola, correct? 2. the a^2 is 49, correct? 3. the b^2 is 72,

80. ## Alg II/Trig

A parabola has a vertex at (0,0); a horizontal axis; and the point (12,6) is on the parabola. Write the equation of the parabola in standard form.

81. ## math

A parabola that has a maximum = -3 at x = -11. Give four things that are true about the parabola based on this information. Include in your discussion the number of x-intercepts (if any) for the parabola.

82. ## math

the vertices are at (2,1) and (2,7) and focus is at (2,*) write the equation of the hyperbola that meets each set of conditions. Is the asterisk supposed to be an 8? It has to be some number. I will set this up for you later of you respond. The fomulas you

83. ## Geometry

Let A and B be two points on the hyperbola xy=1, and let C be the reflection of B through the origin. Let Gamma be the circumcircle of triangle ABC and let A' be the point on Gamma diametrically opposite A. Show that A' is also on the hyperbola xy=1.

84. ## Algebra

The focus of a parabola is (0,−4) . The directrix of the parabola is the line y=−5 . What is the equation of the parabola? y=−1/4x^2+4 y=1/2x^2−9/2 y=−1/2x^2−9/2 y=1/4x^2−4

85. ## math

Find a parametrisation of the hyperbola that is obtained by translating the hyperbola with equation 9x^2 - (y^2)/16 =1 by -2 unit(s) right and 4 unit(s) up x=? y=?

86. ## Algebra II

Write 36x^2-360x-25y^2-100y=100 in standard form. Then state whether the graphs of the equation is a parabola, circle, ellipse, or hyperbola. I started with: 36(x^2 -10x+25)-25(y^2+4y+4)=100+36(25)-25(4) which leads to: 36(x^2-10x+25)/900 -

87. ## Algebra

The directrix of a parabola is y=−4 . The focus of the parabola is (−2,−2) . What is the equation of the parabola? y=1/4(x+2)^2−3 y=1/8(x−2)^2−3 y=−1/8(x+2)^2+3 y=−1/4(x−2)^2−3

88. ## precalculus

How is the equation of a hyperbola and an ellipse related?How are the graphs of an ellipse and a hyperbola similiar and different?

89. ## MATHS

a parabola passes through the points (1,1) , (2,0) and (3,1) the equation of the parabola is y=ax^2 + bx + c a) write down a system of equations representing this parabola. b) solve the corresponding system and hence write down the equation of the parabola

90. ## algebra

find an equation that models the path of a satelite if its path is a hyperbola, a=55,000km and c=81,000km assume that the center of the hyperbola is the origin and the tranverse axis is horizontal

91. ## math

The focal points of a hyperbola are (0,6) and (0,-6), and the point (5,6) is on one of its branches. Find coordinates for the points where the hyperbola intersects its major axis. Also find equations for the asymptotes, and use them to help you draw the

92. ## precalculus

graph the parabola y=2x^2-6x-3. plot point on the parabola A[1,-7] and draw a line through A with an angle of inclination equal to 30 degrees. then find the equation of the line and its second point of intersection B, with the parabola

93. ## precal

complete the square to identify what type of conic you have, identify the key parts indicated and then graph conic. parabola: vertex,focus, directrix, focal diameter. ellipse: center,vertices, foci, eccentricity. hyperbola: center, vertices, foci, slope of

94. ## maths

consider the line y=6x-k and the parabola y=x^2 i) for what value of k is the line y=6x-k a tangent to the parabola y=x^2 ? ii) the line y=6x-k intersects the parabola in two distinct places. what is the largest integer value that k can take ?

95. ## precalc

Let F = (0,9) be the focus and the line y = 1 be the directrix. Plot several points P that are three times as far from the focus as they are from the directrix, including the vertices on the y-axis. The configuration of all such P is a hyperbola of

96. ## Algebra

The reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 60 inches wide and 30 inches deep, how far from the vertex should the microphone

97. ## ALGEBRA 1

Please check for me.Without drawing the graph of the given equation determine (a)how many x-intercepts the parabola has (b)whether it vertex lies above, below or on the axis. 1. y=x^2-5x+6 I use the determinant sqrt b^2 -4ac (-5)^2-4(1)(6))=1 There are two

98. ## ALGEBRA 1

Please check for me.Without drawing the graph of the given equation determine (a)how many x-intercepts the parabola has (b)whether it vertex lies above, below or on the axis. 1. y=x^2-5x+6 I use the determinant sqrt b^2 -4ac (-5)^2-4(1)(6))=1 There are two

99. ## MATH! Urgent

umm suppose a parabola has a vertex at (0,2) and points (1,1) how would I derive the equation and focus, i've been trying to understand this for so long, I can't get it. Does this parabola have the equation (y-2)^2 = x and a focus of 1/4?? Is that

100. ## math

Tshabalala wants to reconstruct his farm to separate his sheep and goats. Therefore he decided to enclose a rectangular field with a fence and divide it into two smaller rectangular fields by constructing another fence parallel to one side of the field. He