The equation of the parabola whose vertex and focus lie on the axis of `x` at distances `a` and `a_1` from the origin, respectively, is (a) `y^2-4(a_1-a)x` (b) `y^2-4(a_1-a)(x-a)` (c) `y^2-4(a_1-a)(x-a)` (d) ` n o n e `

Options

A. `y^(2)=4(a_(1)-a)x`
B. `y^(2)=4(a_(1)-a)(x-a)`
C. `y^(2)=4(a_(1)-a)(x-a_(1))`
D. none of these

Answer

B

Explanation

The coordinates of the focus and vertex of the require parabola are `S(a_(1), 0)" and A(a, 0)"` respectively. Therefore, the distance between the vertex and focus is
`AS=a_(1)-a`
`rArr" Length of the L.R.=4"(a_(1)-a)`
Thus, the equation of the parabola referred to dthe vertex as the origin and axis along x-axis is
`y^(2)=4(a_(1)-a)x`
Now, translate the parabola through 'a' units along positive direction of x-axis to obtain
`y^(2)=4(a_(1)-a)(x-a)`
as the equation of the required parabola.