Question

Which is the standard form of the equation of a parabola with a focus of (8, 0) and directrix x = –8?

Answer 1

If your on e2020, its C

Explanation:

y^2=32x, the work above is correct but they forgot to take the square away in the final answer. hope this helps!

Answer 2

with a parabola that faces left or right it is
(y-k)²=4p(x-h)

p is distance from directix to vertex which is also the distance from vertex to focus

if it opens to the right, then p is positive
if it opens to the left, then p is negative

so we know that directix is-8 and focus is (8,0)
directix is behind the parabola
so therfor the parabola opens to the right
distance from x=-8 to (8,0) is 16 units
16/2=8
p=8

vertex is 8 units to right of directix or 8 units to the left of focus
(8,0) is focus so vertex is (0,0)


(h,k) is vertex
(y-k)²=4p(x-h)
(y-0)²=4(16)(x-0)
y²=64x