JEE Main 2022 · 28 Jun · Shift 1 · Mathematics Q13

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MathematicsSingle correct+4 / -1Question 13 of 90

Let the eccentricity of the hyperbola $H:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ be $\sqrt{\dfrac52}$ and length of its latus rectum be $6\sqrt2$ . If $y=2x+c$ is a tangent to the hyperbola H, then the value of $c^2$ is equal to

Answer and worked solution

Official answer: B

Shape. $e^2=\frac52$ gives $b^2=\frac32a^2$ ; $\frac{2b^2}a=6\sqrt2$ gives $b^2=3\sqrt2a$ . So $a=2\sqrt2$ , $a^2=8$ , $b^2=12$ .

Tangency. $c^2=a^2m^2-b^2=32-12=20$ .

(B)

Topics:Hyperbola Tangents and normals to conics

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JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 13