Let the two fixed points be and and let every point satisfy where and are positive…

MATHEMATICS · Multi-part · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let the two fixed points be

F_1(-c,0)

and

F_2(c,0)

and let every point

P(x,y)

satisfy

|PF_2-PF_1|=2a

where

a

and

c

are positive constants with

c>a

. (i) Derive the Cartesian equation of the curve in simplest form. (ii) Express

b

in terms of

a

and

c

. (iii) Write the equations of the asymptotes. (iv) Find the eccentricity of the curve.