Question

Aparabola has the focus at (4,6) and the directrix y = -6. Which equation represents this parabola?

Answer 1

(x-4)^2=24y

Explanation:

I took the test and got it right.

Answer 2

(x - 4)² = 24y

Explanation:

In a parabola with focus at (x, y) and directrix at y = k - p, we can write;

Focus: (h, (k + p))

Directrix: y = k - p

We are given focus at (4, 6)

Thus;

h = 4 &

k + p = 6 - - - (1)

Also, directrix at y = -6

Thus;

k - p = -6 - - - (2)

Adding eq(1) and eq(2) together gives us;

2k = 0

k = 0

Thus, p = 6

The equation takes the formula;

(x - h)² = 4p(y - k)

Plugging in the relevant values;

(x - 4)² = 4(6)(y - 0)

(x - 4)² = 24y