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Question:

If the line xa + yb = √2 touches the ellipse x²/a² + y²/b² = 1, then the eccentric angle θ of point of contact is equal to?

450

900

600

0

Solution:

Equation of any tangent to the ellipse x²/a² + y²/b² = 1 is xa cos θ + yb sin θ = 1.. (1)
Also, xa + yb = √2 (2) touches the given ellipse.
Comparing coefficients in (1) and (2), we get
(cos θ)/a = 1/√2 = (sin θ)/b = 1/√2
∴ cos θ = 1/√2 = sin θ
⇒ θ = 45°
Hence, option A.