Find the standard form of the equation of the parabola with the given characteristics. Focus: (2, 2) Directrix: x = −2

Answer 1

Because the directrix is of the form x = ? the standard form for this parabola will be x = a(y - k)² +h. The focus is (2,2) which has to be of the form (h + 1/4a,k). The formula for the directrix is x = h - 1/4a.

Vertex: (h,k) = (2,2)

h = 2 k = 2

Directrix: x = h - 1/4a

-2 = 2 - 1/4a

1/4a = 2 + 2

1/4a = 4

1 = 4(4a)

1 = 16a

a = 1/16

Putting these values for "a", h and k into our standard form, we get:

x = a(y - k)² + h

x = (1/16)(y - 2)² + 2

Hope this helps!