Question

What is the equation of the quadratic graph with a focus of (4, 3) and a directix of y = 13?

f(x) = −one twentieth (x − 4)2 + 10

f(x) = −one twentieth (x − 4)2 + 8

f(x) = one twentieth (x − 4)2 + 10

f(x) = one twentieth (x + 4)2 + 8

Answer 1

the focus is below the directrix so its concave down...



the distance between the focus and directrix is 2* focal length.

so disstance is 2a = -10 so the focal length is a = -5 units...

so the vertex is (4, 3 - (-5))

so vertex is at (4, 8)

the general form of the equation I use is

\[(x^2 - h) = 4a(y - k)\]

\[(x - 4)^2 = 4\times(-5)(y - 8)\]

just make y the subject for your solution .

hope it helps