Find the standard form of the equation of the parabola satis

Find the standard form of the equation of the parabola satisfying the given conditions. Vertex: (1, -1); Focus:)1, -5)

Solution

distance between vertex and focus =a

a=[(1-1)²+(-1+5)²] =4

equation of parabola with vertex (h,k)=(1,-1) ,a=4

is (x-1)²=-4*4(y-(-1))

(x-1)²=-16(y+1)

x²-2x+1=-16y -16

16y =-x²+2x-17

y=(1/16)(-x²+2x-17)

y=-(1/16)x²+(1/8)x-(17/16)