Coordinate Geometry
Tangent lengths in GP for parabola
MJMT_Full_Test_10
Grade 12
Question:
TP and TQ are tangents to a parabola and $p_1$, $p_2$, $p_3$ are the lengths of perpendiculars from $P$, $T$, $Q$ respectively on any tangent to the parabola. Then $p_1$, $p_2$, $p_3$ are in
A.P
G.P
H.P
None of these
Step-by-Step Solution
Key Concept: Use the standard parametric form. For a tangent to the parabola at parameter $t$: distance from $P=(at_1^2,2at_1)$, $T$, and $Q=(at_2^2,2at_2)$ can be computed explicitly.
$p_2^2=p_1\cdot p_3$, so they are in GP.
Correct Answer: 2