What is the equation of a parabola with a focus of (8,2) and a directrix of x=6?
1. 4(x-7)=(y-2)²
2. 4(x+7)=(y+2)²
3. 4(x-2)=(y-7)²
4. 4(x+2)=(y+7)²
show

Distance of a point (x,y) from focus = its distance from the directrix so

sqrt[(x-8)^2 + (y - 2)^2] = x - 6

squaring both sides:-

x^2 - 16x + 64 + y^2 -4y + 4 = x^2 -12x + 36

y^2 - 4y  = 4x - 32

(y-2)^2 - 4 = 4x - 32

(y - 2)62 = 4x - 28

(y - 2)^2 = 4(x - 7)

No. 1 is the correct choice