Question

What is the equation of the quadratic graph with a focus of (2, - 2) and a directrix of y = 0?

A f(x) = - + (x - 2)2 - 1
B 12) = - * (x = 232 + 1
C f(x) = - (x = 232
Df(x) = } (x - 2)2 + 1

Answer 1

f(x) = -(1/4)(x - 2)^2 - 1

Explanation:

Take any point (x,y) on the graph.

The distance of this point from the focus is equal to the distance of the point from the directrix.

So √ [(x - 2)^2 + (y + 2)^2 ] = y

(x - 2)^2 + (y + 2)^2 = y^2

(x - 2)^2 + y^2 + 4y + 4 = y^2

(x - 2)^2 + 4y + 4 = 0

4y = -(x - 2)^2 - 4

y = -(1/4)(x - 2)^2 - 1 (answer).