The straight lines joining any point `P` on the parabola `y^2=4a x` to the vertex and perpendicular from the focus to the tangent at `P` intersect at `Rdot` Then the equation of the locus of `R` is
(a)`x^2+2y^2-a x=0` (b)`2x^2+y^2-2a x=0` (c)`2x^2+2y^2-a y=0` (d) `2x^2+y^2-2a y=0`

Options

A. `x^(2)+2y^(2)-ax=0`
B. `2x^(2)+y^(2)-ax=0`
C. `2x^(2)+2y^(2)-ay=0`
D. `2x^(2)+y^(2)-ay=0`

Answer

B

Explanation

(2) Tangent at point P is `ty=x+at^(2)`.
The line perpendicular to (1) passes through (a,0). Therefore,
y-0=-t(x-1)
`ortx+y=ta`
`ory=t(a-x)` (1)
The equation of OP is
`y-(2)/(t)x=0ory=(2)/(t)x` (3)
From (2) and (3), eliminating
t,we get
`y^(2)=2x(a-x)`
`or2x^(2)+y^(2)ax=0`