Consider an ellipse `x^2/25+y^2/9=1` with centre c and a point P on it with eccentric angle `pi/4.` Nomal drawn at P intersects the major and minor axes in `A and B` respectively. `N_1 and N_2` are the feet of the perpendiculars from the foci `S_1 and S_2` respectively on the tangent at P and N is the foot of the perpendicular from the centre of the ellipse on the normal at P. Tangent at P intersects the axis of x at T.

Options

A. `{:(P,Q,R,S),(2,3,4,1):}`
B. `{:(P,Q,R,S),(3,1,4,2):}`
C. `{:(P,Q,R,S),(2,4,1,3):}`
D. `{:(P,Q,R,S),(4,1,2,3):}`

Answer

C

Explanation

(p) `(CA)(CT) = (e^(2)a cos theta) ((a^(2))/(a cos theta)) = a^(2) -b^(2) = 16`
(q) `(PN) (PB) = a^(2) = 25`
(r) `(S_(1)N_(1)) (S_(2)N_(2)) = b^(2) = 9`
(s) `(S_(1)P) (S_(2)P) = [a + e(a cos theta)] [a-e(a cos theta)] = a^(2) sin^(2) theta + b^(2) cos^(2) theta = 17`