Ellipse and Hyperbola: JEE Main MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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JEE MainHardQuestion 400007

Question

The tangent at (a cos θ, b sin θ) to the ellipse x²/a² + y²/b² = 1 is:

A
(x cos θ)/a + (y sin θ)/b = 1
Correct
B
x cos θ/a − y sin θ/b = 1
C
x/a + y/b = 1
D
x cos θ + y sin θ = 1

Correct answer

(x cos θ)/a + (y sin θ)/b = 1

Explanation

Using T = 0 formula: tangent at (x₁, y₁) to ellipse: xx₁/a² + yy₁/b² = 1. At parametric point (a cos θ, b sin θ): x(a cos θ)/a² + y(b sin θ)/b² = 1 → (x cos θ)/a + (y sin θ)/b = 1.

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