JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q10

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MathematicsSingle correct+4 / -1Question 10 of 90

Let $P:y^2=4ax$ , $a>0$ be a parabola with focus S. Let the tangents to the parabola P make an angle of $\dfrac\pi4$ with the line $y=3x+5$ touch the parabola P at A and B. Then the value of $a$ for which A, B and S are collinear is

8 only

2 only

\dfrac14

only

any

a>0

Answer and worked solution

Official answer: D

Slopes at $45°$ to slope 3: $m=\frac12$ or $-2$ . Contact points $\left(\frac a{m^2},\frac{2a}m\right)$ : $(4a,4a)$ and $\left(\frac a4,-a\right)$ .

Collinear with $S(a,0)$ : both slopes from S are $\frac43$ , for every $a>0$ .

(D)

Topics:Tangents and normals to conics Parabola

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JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 10