The tangents to x 2 + y 2 = a 2 having inclinations α and β intersect at P . If cot α + cot β = 0 , then the locus of P is

Question

The tangents to x 2 + y 2 = a 2 having inclinations α and β intersect at P . If cot α + cot β = 0 , then the locus of P is, x + y = 0, x - y = 0, x y = 0, None of these

MARKS App · Accepted Answer

Equation of tangent in slope form y = m x ± a 1 + m 2 k - m h 2 = a 2 1 + m 2 m 2 h 2 - a 2 - 2 m h k + k 2 - a 2 = 0 m 1 + m 2 = 2 h k h 2 - a 2 , m 1 m 2 = k 2 - a 2 h 2 - a 2 cot ⁡ α + cot ⁡ β = 0 1 tan ⁡ α + 1 tan ⁡ β = 0 ⇒ tan ⁡ α + tan ⁡ β tan ⁡ α tan ⁡ β = 0 2 h k = 0 ⇒ x y = 0

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