Question

Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1

Answer 1

Explanation:

eq. of directrix is y-1=0

let (x,y) be any point the parabola.

then\sqrt{ (x-6)^2+(y-2)^2}=\frac{y-1}{(-1)*2}

squaring

x²-12x+36+y²-4y+4=y²-2y+1

x²-12 x+40-1=4y-2y

2y=x²-12x+39=x²-12x+36+3

(x-6)²=2y-3

Answer 2

f(x)= 1/2(x-6)^2+3/2

hope this helped