standard form of a parabola

Question

Find the standard form of the parabola whose focus is (3,2) and directrix is x=-1

a x=1/12(y-1)^2+2

b x= 1/12 (y-2)^2+1

c x= 1/8 (y-2)^2 +1

d x=1/8(y-1)^2+2

Answer 1

The standard form of a parabola opening to the right is 4p(x-h) =(y-k)²

p is the focal length. This is 1/2 the distance from the directrix to the focal point = (3-(-1))/2 = 2

(h,k) is the apex which is 1/2 way between focal length and directrix in x and with the same y as the focal point, so (1,2). The equation becomes 8(x-1) = (y-2)² or x = (1/8)(y-2)² + 1

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