Question

The tangents to x² + y² = a² having inclinations a and b intersect at P. If cot a + cot b = 0 then the locus of P is –

• A. x + y = 0
• B. x – y = 0
• C. xy = 0
• D. None of these

Answer 1

Answer: (C)

xy = 0

Answer 2

equation of tangent in slope form

y = mx ± a $\sqrt { 1 + \mathrm { m } ^ { 2 } }$

(k –mh)² = a²(1 + m²)

m²(h² – a²) – 2mhk + k² – a² = 0

m₁ + m₂ = $\frac { 2 h k } { h ^ { 2 } - a ^ { 2 } }$ , m₁m₂ =

cot a + cot b = 0

$\frac { 1 } { \tan \alpha }$ + $\frac { 1 } { \tan \beta }$ = 0 Ž $\frac { \tan \alpha + \tan \beta } { \tan \alpha \tan \beta }$ = 0

2hk = 0

Ž xy = 0