BITSAT 2017 Slot 2 Solved Paper

Let the ellipse be

x2

a2

+

y2

b2

=1
and let

x‌cos‌θ

a

+

y‌sin‌θ

b

=1 ......(i)
be a tangent to it at point (a‌cos‌θ,b‌sin‌θ). Then, p= length of the perpendicular from S(ae,0) on Eq. (i)
⇒p=|

e‌cos‌θ−1

√ cos2θ a2 + sin2θ b2

|
p′= length of the perpendicular from O(0,0) on Eq. (i)
⇒p′=|

1

√ cos2θ a2 + sin2θ b2

|
and r=ae‌cos‌θ−a
Clearly, rp′=ap