JEE Main 2022 · 26 Jun · Shift 1 · Mathematics Q13

← JEE Main 2022 · 26 Jun · Shift 1

MathematicsSingle correct+4 / -1Question 13 of 90

Let the normal at the point P on the parabola $y^2=6x$ pass through the point $(5,-8)$ . If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is :

-3

-\dfrac94

-\dfrac52

-2

Answer and worked solution

Official answer: B

Normal to $y^2=6x$ ( $a=\frac32$ ) at $(at^2,2at)$ : $y=-tx+2at+at^3$ . Through $(5,-8)$ : $3t^3-4t+16=0$ , so $t=-2$ and $P=(6,-6)$ .

Tangent at P. $ty=x+at^2$ : $-2y=x+6$ .

Directrix $x=-\frac32$ : $-2y=\frac92$ , $y=-\dfrac94$ .

(B)

Topics:Parabola Tangents and normals to conics

← Previous question Next question →

JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 13