• question_answer Let P,Q and R be three conformal points on the parabola ${{y}^{2}}=4ax$. Then, the correct statement is A)  circle circumscribing the $\Delta PQR$ passes through the vertex of the parabola. B)  the algebraic sum of slopes of the tangents at P, Q and R vanishes. C)  the algebraic sum of the ordinates of the points P vanishes. D)  circumcentre of $\Delta PQR$ lies on the axis of the parabola.

Since, the line $\frac{x}{e}+\frac{y}{e'}=1$ touches the circle  ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$. $\therefore$    $\frac{1}{\sqrt{\frac{1}{{{e}^{2}}}+\frac{1}{e{{'}^{2}}}}}=2$ $\Rightarrow$            $a=\frac{ee'}{\sqrt{{{e}^{2}}+e{{'}^{2}}}}=2$        [from Eq. (i)]