# Pre-calc

Heres the equation:
(x^2)-(4y^2)-(4x)+(24y)-(36)=0
Your supposed to find the coordinates of the center, foci, and vertices, and the equations of the asymptotes of its graph.
So first you complete the square right?
(x^2 -4x+4)-4(y^2 +6y+9)=36+4+36
[((x+2)^2)/76] -[(y+3)^2)/19]=1
So its a hyperbola, and is the center at (-2, -3)??

1. 👍 0
2. 👎 0
3. 👁 402
1. Picking it up from your

(x^2 -4x+4)-4(y^2 +6y+9)=36+4+36
should have been
(x^2 -4x+4)-4(y^2 +6y+9)=36+4+36
notice on the left you had
... 4(..... +9) , so you subtracted 36, thus you must subtract 36 from the right side as well

final version

(x-2)^2 - 4(y-3)^2 = 36

or

(x-2)^2 /36 - (y-3)^2 /9 = 1

centre would be (2,3)
a = 1 , b = 3 , c = √10

vertices: (1,3) and (3,3)
foci :( 2-√10 , 3) and (2+√10 , 3)
asymptotes:

first: y = 3x + b , with (2,3) on it
3 = 6+b
b = -3 ----> y = 3x - 3
second: y = -3x + b
3 = -6+b
b = 9 -----> y = -3x + 9

1. 👍 0
2. 👎 0
(x^2 -4x+4)-4(y^2 +6y+9)=36+4+36
should be (x^2 -4x+4)-4(y^2 -6y+9)=36+4-36
(x^2 -4x+4)/4-4(y^2 -6y+9)/4=4/4
((x-2)^2)/4- (y-3)^2 =1
hyperbola, center at (2,3)

1. 👍 0
2. 👎 0
3. from
(x-2)^2 /36 - (y-3)^2 /9 = 1 , the rest should say

centre is (2,3)
a = 6, b = 3, c = √45

vertices: (-4,3) and (8,3)
foci :( 2-√45 , 3) and (2+√45 , 3)
asymptotes:

first: y = (1/2)x + b , with (2,3) on it
3 = 1+b
b = 2 ----> y = (1/2)x + 2
second: y = -(1/2)x + b
3 = 1+b
b = 2 -----> y = -(1/2)x + 2

check my arithmetic

1. 👍 0
2. 👎 0
4. Thank you guys so much :)

1. 👍 0
2. 👎 0
5. I am sorry, don't know where I got that -4 on the RS from
(x^2 -4x+4)-4(y^2 -6y+9)=36+4-36

((x-2)^2)/4- (y-3)^2 =1

from there, a=2, b = 1, c = √5

1. 👍 0
2. 👎 0
6. Haha ok i totally get it thanks!

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math

Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down. A)Write the coordinated of the vertices of the image after reflection. B)Write a rule for the translation. Use arrow rotation.

2. ### Algebra

For the equation 9x^2+4y^2+54x-8y+49=0 determine the center, vertices and foci?

3. ### Math

9x^2+16y^2-18x+64y-71=0 find the coordinates of the center, the foci, and the vertices of this ellipse. 9x^2+16y^2-18x+64y-71=0 9x^2-18x+16y^2+64y=71 9(x^2-2x)+16(y^2+4y)=71 9(x^2-2x+1)+16(y^2+4y+4)=71

4. ### Math

Find an equation for the ellipse. center:(3,2) a=3c Foci:(1,2)(5,2) h=3 k=2 I do not know where to start.

1. ### Help with triangle

I need help with these: Triangle LMN has vertices L(-6,5), M(-4,-3), N(-2,4). Find the coordinates of the vertices of its image after it is reflected over the x-axis and then translated by (-3,0) a. L(-9,-5), M(-7,3), N(-5,-4) b.

2. ### geometry

Triangle PQR has vertices P(1,2), Q(25,2) and R(10,20). Find the coordinates of the centroid. Find the coordinates of the circumcenter. Find the coordinates of the orthocenter. Find the equation of the line.

3. ### math

Find the center, foci, and vertices of this hyperbola 16x^2-y^2-32x+8y+16=0

4. ### Algebra2

What are the vertices, foci, and asymptotes of the hyperbola with the equation 16x^2-4y^2=64? What would the formulas be to find the answers?

1. ### Math

Find the center, vertices, foci, and eccentricity of the ellipse. 9x^2 + 4y^2 - 36x + 8y + 31 = 0 I know the center is (2,-1) For the vertices I had (3,-1)(1,-1) and the foci (3.8,-1)(.20,-1) and e = 1.80 but I think these are

2. ### Math, precalculus

Write an equation for the hyperbola with vertices (7,5),(-5,5); foci (11,5),(-9,5)

3. ### Analytic Geometry

Find the vertices, foci, eccentricity and length of the latus rectum of the ellipse whose equation is x^2 + 9Y^2 = 9

4. ### math

vertices (0,6)and (-10,6) foci(-2,6) (-8,6) write the equation for ellipses