JEE Main 2026 · 6 Apr · Shift 1 · Mathematics Q12

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MathematicsSingle correct+4 / -1Question 12 of 75

Let chord PQ of length $3\sqrt{13}$ of the parabola $y^2=12x$ be such that the ordinates of points P and Q are in the ratio 1:2. If the chord PQ subtends an angle $\alpha$ at the focus of the parabola, then $\sin\alpha$ is equal to:

\dfrac35

\dfrac45

\dfrac5{13}

\dfrac{12}{13}

Answer and worked solution

Official answer: A

Points. Take $P(3t^2,6t)$ and $Q(12t^2,12t)$ (ordinates 1 : 2).

Length.
$PQ^2=81t^4+36t^2=117\ \Rightarrow\ t^2=1.$
So $P(3,6)$ and $Q(12,12)$ , with focus $S(3,0)$ .

Angle at S. $\vec{SP}=(0,6)$ and $\vec{SQ}=(9,12)$ :
$\cos\alpha=\frac{72}{6\cdot15}=\frac45,\qquad\sin\alpha=\frac35.$

(A)

Topics:Parabola Angle between lines

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JEE Main 2026 · 6 Apr · Shift 1, Mathematics question 12