Aparabola has a focus of f(8.5,−4) and a directrix of x=9.5. what is the equation of the parabola? 1. 1/2y2+4y−1=x 2 .1/2y2−4y+1=x 3. −1/2y2+4y−1=x 4. −1/2y2−4y+1=x

Step-by-step explanation:

A parabola has a focus of F(8.5,−4) and a directrix of x=9.5.

General form of  horizontal parabola is

the distance between directrix and focus is the value of p

so p = 8.5 - 9.5 = -0.5

Focus is (h+p , k), given focus is (8.5, -4)

So k = -4 and h+p = 8.5

we know p = -0.5

h +p = 8.5

h - 0.5 = 8.5

so h= 9                   and k = -4

vertex is (h,k) that is (9, -4)

Now plug in the value in the general equation

, k= -4, h= 9 , p = -0.5

subtract 18 on both sides

Divide whole equation by -2