The tangents to having inclinations and intersect at

MATHEMATICS · Single correct · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

The tangents to

x^2 + y^2 = a^2

having inclinations

\alpha

and

\beta

intersect at

P

. If

\cot \alpha + \cot \beta = 0

, then the locus of

P

is (1)

x + y = 0

(2)

x - y = 0

(3)

xy = 0

(4)

xy = 1