Find the standard equation of the parabola.

Question

A parabola has focus F (-2, -5) and directrix x = 6

Answer 1

it's a left ward opening parabola because the focus is to

the left of the directrix

general form is x= a(y-k)^2+ h

where (h,k) is the vertex, half way between focus and directrix

axis of symmetry is y = 2, where h=2, k=-5

x=a(y+5)^2 + 2

plug in another point on the parabola to solve for "a"

distance from focus to a point on the parabola = distance from that point to the directrix. Go up vertically from (2,-5) to (-2,3)

(-2,3) is a point on the parabola because it is 8 units above the focus and 8 units to the left from the directrix

x = a(y+5)^2 +2

-2 = a(3+5)^2 +2

64a = -4

a =-4/64 = -1/16

the parabola equation is:

x = (-1/16)(y+5)^2 + 2

or 16x = -(y+5)^2 + 32

or 16x = -y^2 - 10y + 7

Answer 2

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