JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q13

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MathematicsSingle correct+4 / -1Question 13 of 90

Let the tangent drawn to the parabola $y^2=24x$ at the point $(\alpha,\beta)$ is perpendicular to the line $2x+2y=5$ . Then the normal to the hyperbola $\dfrac{x^2}{\alpha^2}-\dfrac{y^2}{\beta^2}=1$ at the point $(\alpha+4,\beta+4)$ does NOT pass through the point :

(25, 10)

(20, 12)

(30, 8)

(15, 13)

Answer and worked solution

Official answer: D

Tangent slope 1 on $y^2=24x$ : $(\alpha,\beta)=(6,12)$ . Hyperbola $\frac{x^2}{36}-\frac{y^2}{144}=1$ at $(10,16)$ .

Normal. $\frac{36x}{10}+\frac{144y}{16}=180$ , i.e. $2x+5y=100$ . (15, 13) gives 95: not on it.

(D)

Topics:Tangents and normals to conics Hyperbola

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JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 13