Question

A parabola can be drawn given a focus of (4,7) and a directrix of y=−3. What can be said about the parabola?

Answer 1

The parabola has a vertex (4,2) and p-value, 5.

How the vertex of a parabola can be found.

For a parabola function

Given that

focus = (4,7) and directrix, y = -3

That's

focus (4,7) = (h, k + p)

directrix ,y = -3 = k-p

Therefore

k + p = 7--------1

k - p = -3 ------2

Solve simultaneously

Add equations 1 & 2

2k = 4

k = 4/2

k = 2

Substitute into k + p = 7

2 + p = 7

p = 7 - 2

p = 5

Vertex = (h,k) = (4, 2)

p- value = 5

So, the parabola has a vertex (4,2) and p-value, 5.