Question

Tangents are drawn to a parabola from a point $T$. If $P,Q$ are the points of contact then perpendicular distance from $P,T$ and $Q$ upon the tangent at the vertex of the parabola are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. none of these

Answer 1

The correct option is B G.P.

Let $P(a{t}_1^2,2at)$, $Q(a{t}_2^2,2a{t}_2)$, then the point of intersection of the tangents at P,
$t_{1}y=x+a{t}_1^2$ and at Q, $t_{2}y=x+a{t}_2^2$ is $T(a{t}_1{t}_2,a(t_1+t_2))$.
Distance of P, T and Q from the vertex are $a{t}_1^2$, $a{t}_1{t}_2$, $a{t}_2^2$ which are in G.P.