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.

Focus: (-1,6); Directrix: y=4

The standard form of the equation is?

Solution

focus :(-1,6)   directrix : y=4

This parabola is of the form

(x-h)²=4p(y-k)

And focus of this formula is (h,k+p)

And on comparing it with given focus we get h= -1 and k+p=6

And directrix of such parabola is y =k-p

Therefore k-p=4

k+p=6 and k-p=4

From these two equations we get

k=5 and p=1

Therefore equation of parabola is

(x+1)²=4(y-5)

x²+2x+1=4y-20

x^2 +2x+21=4y

y= x²/4 + x/2 +21/4