Let a circle of radius be concentric to the ellipse . Then the common tangents are inclined to the minor axis of the ellipse at the angle:

Explanation: Solution Ellipse ki equation: . Yahan aur hai. Circle ki equation ( ): . 1. Tangent ki condition: Ellipse ke liye tangent ki equation: . Circle ke liye tangent ki condition: . Dono common hain, isliye: 2. Angle nikaalein: Slope , toh -axis (major axis) ke saath angle hai. Humein minor axis ( -axis) ke saath inclination nikaalna hai:

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let a circle of radius $4$ be concentric to the ellipse $15x^{2} + 19y^{2} = 285$ . Then the common tangents are inclined to the minor axis of the ellipse at the angle:

Choose the correct answer: