Question

$TP,TQ$ are tangents to a parabola $y^2=4ax,p_1,p_2,p_3$ are the lengths of the perpendicular from $P,T,Q$ respectively on tangent at the vertex, then $p_1,p_2,p_3$ are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. A.G.P.

Answer 1

The correct option is B G.P.

Eq. of tangent through $T(h.k)$ is
$ky=2a(x+h)$
$y=\frac{2a(x+h)}{k}$
$\frac{4a^2(x+h{)}^2}{k^2}=4ax$
$a(x^2+h^2+2hx)=k^{2}x$
$p_1{p}_2=x_1{x}_2$
$x_1{x}_2=h^2$
$\therefore x_1,h,x_2$ are in G.P.