Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0). y = one fourth(x − 5)2 + 1 y = one fourth(x + 1)2 − 5 y = −one fourth(x + 1)2 − 5 y = −one fourth(x − 5)2 + 1

y = -1/4 ( x-5) ^2 +1

Step-by-step explanation:

parabola with a directrix at y = 2 and a focus at (5, 0)

The focus is equal to ( h, k+ 1/(4a))  where ( h,k) is the vertex

The directrix is equal to  y = k - 1/ (4a)

We know h =5 and

0 = k + 1/(4a)

2 = k - 1 /(4a)

Add these two equations together

2 = 2k

k =1

The vertex is ( 5,2)

Now we find a

0 = 1 + 1/(4a)

-1 = 1/(4a)

-4a =1

a = -1/4

The equation for a parabola is

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

y = -1/4 ( x-5) ^2 +1