The equation of the parabola, whose vertex and focus are on the x-axis at distances a and b from the origin respectively, is :

Options

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

Answer

A

Explanation

We have,
AS=Distance between the vertex and focus =b-a

`:." "L.R.=4(b-a)`
So, the equation of the parabola having vertex at the origin and
`L.R.=4(b-a)is`
`y^(2)=4(b-a)x" ...(i)"`
Clearly, required parabola is obtained by translating (i) through distance 'a' along positive direction of x-axis. So, its equation is
`y^(2)=4(b-a)(x-a).`