JEE Main 2022 · 26 Jul · Shift 2 · Mathematics Q11

← JEE Main 2022 · 26 Jul · Shift 2

MathematicsSingle correct+4 / -1Question 11 of 90

The acute angle between the pair of tangents drawn to the ellipse $2x^2+3y^2=5$ from the point $(1,3)$ is

\tan^{-1}\left(\dfrac{16}{7\sqrt5}\right)

\tan^{-1}\left(\dfrac{24}{7\sqrt5}\right)

\tan^{-1}\left(\dfrac{32}{7\sqrt5}\right)

\tan^{-1}\left(\dfrac{3+8\sqrt5}{35}\right)

Answer and worked solution

Official answer: B

Tangent condition. For $\frac{x^2}{5/2}+\frac{y^2}{5/3}=1$ , the line $y=mx+(3-m)$ is tangent when $(3-m)^2=\frac52m^2+\frac53$ , i.e. $9m^2+36m-44=0$ .

Angle. $m_1+m_2=-4$ , $m_1m_2=-\frac{44}9$ , so $|m_1-m_2|=\frac{8\sqrt5}3$ and $\tan\theta=\frac{8\sqrt5/3}{|1-44/9|}=\frac{24}{7\sqrt5}$ .

(B)

Topics:Tangents and normals to conics Ellipse Angle between lines

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JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 11