Hii,

The answer for this will be y^2 = 4(b−a)(x−a) .

we'll get this equation after undertaking the following steps:

Given, Vertex A is (a,0)

Focus is (b,0)

Distance between vertex and focus AS = b−a=A (say)

So, the equation of parabola with vertex at (a,0) is
(y−0)^2 = 4A(x−a)(y−0)^2 = 4A(x−a)
= (y−0)^2 = 4(b−a)(x−a)⇒(y−0)^2 = 4(b−a)(x−a)
= y^2 = 4(b−a)(x−a)

= y^2 = 4(b−a)(x−a)

Hope this helps.