If is a variable point and

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

A(z)

is a variable point and

B(z_1)

C(z_2)

are fixed point such that

\arg\left(\frac{z-z_1}{z_2-z_1}\right) = \theta_1

and

\arg\left(\frac{z_1-z_2}{z-z_2}\right) = \theta_2

. If

\frac{\tan \theta_1/2}{\tan \theta_2/2} = \frac{3}{2}

, then locus of

A

is branch of hyperbola of eccentricity equal to - - -