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Tangents are drawn from P(-sqrt(3), sqrt(2)) to the ellipse 4x² + y² = 4. Statement-1: these tangents are mutually perpendicular. Statement-2: the locus of points from which mutually perpendicular tangents can be drawn to this ellipse is x² + y² = 5. Choose the correct option.

1. Statement-1 is True, Statement-2 is True and is a correct explanation of Statement-1
2. Statement-1 is True, Statement-2 is True but is NOT a correct explanation of Statement-1
3. Statement-1 is True, Statement-2 is False
4. Statement-1 is False, Statement-2 is True

Correct answer: Statement-1 is True, Statement-2 is True and is a correct explanation of Statement-1

Solution

The director circle of 4x²+y²=4 is x²+y² = 1+4 = 5; P = (-sqrt3, sqrt2) gives 3+2 = 5, so P lies on it and the tangents are perpendicular; Statement-2 correctly explains Statement-1.

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