Question

What is the equation of a parabola with a focus (2,4) and directrix y = 0?

Answer 1

Answer:

The equation of the parabola is (x-2)^2 =8(y-2)

Step-by-step explanation:

Given focus is (2,4) and the directrix is y=0 so the parabola axis is parallel to y- axis.

Focus is (α,β+a) and the directrix is of the form y = β-a

so given  focus is (2,4) compare (α,β+a)

                  here β+a = 4 and a=2 and β=2

now given directrix y = β-a = 2-2 = 0

now the general parabola is (x-α)^2 =4a(y-β) ...(1)

now substitute α =2 ,β=2 and a=2 above equation

The equation of the parabola is (x-2)^2 =8(y-2)