Let and be two points with

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

Problem

Let

F_1(0,-c)

and

F_2(0,c)

be two points with

c>a>0

. Show that the locus of a point

P(x,y)

satisfying

|PF_2-PF_1|=2a

\frac{y^2}{a^2}-\frac{x^2}{c^2-a^2}=1.