Question

Suppose the normal at any point P on the ellipse x²/a² + y²/b² = 1  meets the major axis at G and the minor axis at g. CF is drawn perpendicular to the normal where C is the centre of the ellipse. Then

(a) PF. PG = b²

(b)  PF.PG = a²

(c) PG.pg = SP.S'p

(d)  CG.CT = CS² 

 where S is the focus

Answer 1

Correct option (a),(b),(c),(d)

Explanation :

See Fig. Let P be (cos θ, sinθ). The normal at P is

ax/cosθ - by/sinθ = a² - b²

^Therefore

We have PF = CT = perpendicular distance of C from the tangent at P which is given by

Therefore

PG.pg = SP.S'P

(d) We have