math

Draw a diagram to show that there are two tangent lines to the parabola
y = x2
that pass through the point
(0, −25).
Find the coordinates of the points where these tangent lines intersect the parabola.

  1. 👍 0
  2. 👎 0
  3. 👁 1,522
  1. the parabola y=x² has it's vertex at (0,0).
    Tangent to parabola has slope
    dy/dx=2x, at point (±x, x²).

    For tangents to pass through (0,-25), we have the slope joining (0,-25) and (x,x²) equal to 2x.

    Slope=(y2-y1)/(x2-x1)
    =>
    (x^2-(-25))/(x-0)=dy/dx=2x
    solving for x, we get
    x=+5 or x=-5.
    Thus the tangent points are
    (5,25) and (-5,25).

    1. 👍 2
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus 2

    Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the x-axis.

  2. calculus

    Find equations for two lines through the origin that are tangent to the ellipse 7x2−168x+y2+62=0 please show me the steps :)

  3. Calculus...URGENT..show steps please

    Use implicit differentiation to find the points where the parabola defined by x^{2}-2xy+y^{2}-6x+2y+17 = 0 has horizontal and vertical tangent lines. List your answers as points in the form (a,b).

  4. calculous

    Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (4, 64), and the x-axis.

  1. Math

    Draw two number lines that show 0.20 and 1/5 are equivalent

  2. microeconomics

    The cost of producing flat-screen TVs has fallen over the past decade. Let’s consider some implications of this fact. A.) Draw a supply-and-demand diagram to show the effect of fallen production costs on the price and quantity

  3. calculus 2

    Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (3, 45), and the x-axis.

  4. Mathematics

    Use implicit differentiation to find the points where the parabola defined by x2−2xy+y2−4y+4=0 has horizontal and vertical tangent lines. The parabola has horizontal tangent lines at the point(s) (x-y)/x-y+2 . The parabola has

  1. math

    Consider the parabola y = 6x − x2. (a) Find the slope of the tangent line to the parabola at the point (1, 5). 4 (b) Find an equation of the tangent line in part (a). y =

  2. Geometry - Circles and tangents

    Two circles of radius 1 are externally tangent at Q . Let PQ and QR be diameters of the two circles. From P a tangent is drawn to the circle with diameter QR , and from R a parallel tangent is drawn to the circle with diameter PQ

  3. Geometry

    Prove that the tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a two-column proof. Hint draw a DIAGRAM with the points labeled. Can

  4. math

    Consider the parabola y = 6x − x2. (a) Find the slope of the tangent line to the parabola at the point (1, 5)

You can view more similar questions or ask a new question.