Question

Derive the equation of the parabola with a focus at (4, −7) and a directrix of y = −15. Put the equation in standard form

Answer 1

f(x) = one sixteenthx2 − 8x + 11

f(x) = one sixteenthx2 − 8x − 10

f(x) = one sixteenthx2 − one halfx + 11

f(x) = one sixteenthx2 − one halfx − 10

Answer 2

well the distance between the focus and directrix is twice to focal length

so from y = -7 to y = -15 is 8 units... so the focal length is 4

the vertex is a focal length below the focus...



so know you know the focal length and vertex, you can find the equation,

hope this helps

Answer 3

then the equation is

\[y = \frac{1}{4a}(x - h)^2 + k\]

you know the value of a, the focal length and you know the vertex (h, k)

just substitute and evalute