Question

Equation for a parabola with a focus of (2, -2) and a directrix of y=-8

Answer 1

Y=1/8(x^2+4x+44) is correct

Answer 2

Answer:

y=1/8(-x^2+4x+44

Step-by-step explanation:

In this question the given focus is (2,4) and a directrix of y = 8 and we have to derive the equation of the parabola.

Let (x,y) is a point on the given parabola.Then the distance between the point (x,y) to (2,4) and the distance from (x,y) to diractrix will be same.

Distance between (x,y) and (2,4)

= √(x-2)²+(y-4)²

And the distance between (x,y) and directrix y=8

= (y-8)

Now √(x-2)²+(y-4)² = (y-8)

(x-2)²+(y-4)² = (y-8)²

x²+4-4x+y²+16-8y = y²+64-16y

x²+20+y²-4x-8y = y²-16y+64

x²+20-4x-8y+16y-64=0

x²+8y-4x-44 = 0

8y = -x²+4x+44