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)
