JEE Main 2016 · 10 Apr · Shift 1 · Mathematics Q81

← JEE Main 2016 · 10 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 81 of 90

P and Q are two distinct points on the parabola, $y^2=4x$ , with parameters t and $t_1$ respectively. If the normal at P passes through Q, then the minimum value of $t_1^2$ is :

Answer and worked solution

Official answer: D

The normal at t meets the parabola again at $t_1=-t-\frac2t$ , so $t_1^2=t^2+\frac4{t^2}+4\ge8$ , with equality at $t^2=2$ .

Topics:Tangents and normals to conics Parabola

← Previous question Next question →

JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 81