Question

PLEASE HELP ME I REALLY WOULD APPRECIATE IT!!!!!! Using a directrix of y = −3 and a focus of (2, 1), what quadratic function is created?

Answer 1

Answer:

y = (1/8)x^2 - (1/2)x - 1/2.

Step-by-step explanation:

The graph is a parabola.

The distance from any point on the graph to the focus and to the directrix are equal. So:

sqrt ( (x - 2)^2 + (y - 1)^2 ) = y - (-3)

Squaring both sides:

(x - 2)^2 + (y - 1)^2 = (y + 3)^2

x^2 - 4x + 4 + y^2 - 2y + 1 =  y^2 + 6y + 9

x^2 - 4x + 5 - 9 = y^2 - y^2 + 2y + 6y

8y = x^2 - 4x - 4

y = (1/8)x^2 - (1/2)x - 1/2  is the required quadratic function.