question_answer

The straight line joining any point P on the parabola \[{{y}^{2}}=4ax\]to the vertex and perpendicular from the focus to the tangent at P, intersect at R, then the equation of the locus of R is

A)  \[{{x}^{2}}+2{{y}^{2}}-ax=0\]

B)  \[2{{x}^{2}}+{{y}^{2}}-2ax=0\]

C)  \[2{{x}^{2}}+2{{y}^{2}}-ay=0~\]

D)  \[2{{x}^{2}}+{{y}^{2}}-2ay=0\]

Correct Answer: B

Solution :

 \[T:ty=x+a{{t}^{2}}\] Line perpendicular to (1) through (a, 0) is tx + y = ta                                                            ?(2) Equation of OP\[:y-\frac{2}{t}x=0\]                         ?(3) From eq. (2) and (3) eliminating t we get locus