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Coordinate Geometry

Ellipse, Tangents

jee_main_2026_april_4_shift_1

Grade 12

Question:

The equation of the tangent to the ellipse x^2/16 + y^2/9 = 1 at (4 cos θ, 3 sin θ) is:

A. x cos θ/4 + y sin θ/3 = 1

B. x sin θ/4 + y cos θ/3 = 1

C. x cos θ/3 + y sin θ/4 = 1

D. x sin θ/3 + y cos θ/4 = 1

Step-by-Step Solution

Key Concept: Tangent to x^2/a^2 + y^2/b^2 = 1 at (a cos θ, b sin θ) is x cos θ/a + y sin θ/b = 1.

Step 1: a = 4, b = 3. Tangent: x cos θ/4 + y sin θ/3 = 1.

Correct Answer: A

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