Using a directrix of y=-2 and a focus of (1, 6), what quadratic function is created?

1 Answer
Aniketh N.
Nov 23, 2016

y= x^2/16-x/8+33/16

Explanation:

sqrt((x-1)^2+(y-6)^2)= sqrt((y+2)^2
Square both sides
(x-1)^2+(y-6)^2=(y+2)^2
subtract (y-6)^2 on both sides
(x-1)^2=(y+2)^2-(y-6)^2
Expand both sides
x^2-2x+1=y^2+4y+4-(y^2-12y+36)
Remove like terms on the right side
x^2-2x+1=16y-32
Add 32 to both sides
x^2-2x+33=16y
Divide both sides by 16
x^2/16-(2x/16)+33/16=y
You can reduce the 2x/16 to x/8 '
So your final answer is x^2/16-x/8+33/16=y

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