If normal are drawn from a point `P(h , k)` to the parabola `y^2=4a x` , then the sum of the intercepts which the normals cut-off from the axis of the parabola is

Options

A. (a) `(h+c)`
B. (b) `3(h+a)`
C. (c)`2(h+a)`
D. (d) none of these

Explanation

let `x_1, x_2, x_3` be the intercept on the axis of parabola

eqn of normal `y = mx-2am-am^3`

`y=0`

`mx= 2am+ am^3`

`x= 2a+am^2`

`x_1=2a+ am_1^2`

`x_2= 2a+am_2^2 & x_3= 2a+ am_3^2`

eqn of normal at p(h,k)

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