JEE Main 2026 · 5 Apr · Shift 2 · Mathematics Q12

← JEE Main 2026 · 5 Apr · Shift 2

MathematicsSingle correct+4 / -1Question 12 of 75

Let the directrix of the parabola $P:y^2=8x$ , cut $x$ -axis at the point A. Let $B(\alpha,\beta)$ , $\alpha>1$ , be a point on P such that the slope of AB is $3/5$ . If BC is a focal chord of P, then six times the area of $\Delta ABC$ is :

160

174

192

Answer and worked solution

Official answer: B

Setup. $a=2$ , so $A=(-2,0)$ . Take $B=(2t^2,4t)$ .

Slope. $\dfrac{4t}{2t^2+2}=\dfrac35$ gives $3t^2-10t+3=0$ , so $t=3$ or $\tfrac13$ . Since $\alpha>1$ , $t=3$ and $B=(18,12)$ .

Focal chord. C has parameter $-\tfrac1t=-\tfrac13$ , so $C=\left(\tfrac29,-\tfrac43\right)$ .

Area.
$\tfrac12\left|-2\left(12+\tfrac43\right)+18\left(-\tfrac43\right)+\tfrac29(-12)\right|=\tfrac12\cdot\tfrac{160}3=\tfrac{80}3.$

Six times: 160.

(B)

Topics:Parabola

← Previous question Next question →

JEE Main 2026 · 5 Apr · Shift 2, Mathematics question 12