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: (14,0); Directrix: x=-14

The standard form of the equation is?

Solution

focus=(14,0)      directrix x=-14

This parabola is of the form

(y-k)²=4p(x-h)

where focus = (h+p,k)

And on comparing it with given focus we get k=0 and h+p=14

And directrix   x=h-p

And on comparing it with given directrix

we get

h-p=-14

h+p=14    and h-p=-14

from these two equations we get

h=0    and p=14

Therefore the equation of parabola is

y²= 56x