Equation of parabola with directrix

Question

Find the standard form of the equation of the parabola with directrix y=-1.

Answer 1

directrix: y=-1, v(h,k)

y=a(x-h)^2 +k

for an upward opening parabola, a>0

f(h, 2k+1) distance from f to v = distance from v to directrix which is k+1, so add k+1 to k to get 2k+1

another point on the parabola is (h,2k+1) if the vertex is (h,9) then the focus is (h,19) as 10 is the distance from v to f and from v to the directrix y=-1 k=9 then 2k+1 =19

plug it in to solve for "a"

k+1=a(2k+2)^2 +k= 4a(k+1)^2 +k

a=1/4(k+1)^2

y= (1/4(k+1)^2)(x-h)^2 +k