The base of a triangle is fixed and its vertex moves such that ( )

MATHEMATICS · Subjective · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

The base

AB

of a triangle is fixed and its vertex

C

moves such that

\sin A = k \sin B

(

k \neq 1

). Show that the locus of

C

is a circle whose centre lies on the line

AB

and whose radius is equal to

\frac{ak}{(1-k^2)}

a

being the length of the base

AB