If the normal at any point `P` on the ellipse `x^2/a^2 + y^2/b^2 = 1` cuts the major and minor axes in `L and M` respectively and if `C` is the centre, then `a^2 CL^2 + b^2 CM^2 =` (A) `(a-b)` (B) `(a^2 - b^2)` (C) `(a+b)` (D) `(a^2 + b^2)`

If the normal at any point P of the ellipse x^2/a^2 + y^2/b^2 = 1 meets the major and minor axes at G and E respectively, and if CF is perpendicular upon this normal from the centre C of the ellipse, show that PF.PG=b^2 and PF.PE=a^2 .

The tangent at point P on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 cuts the minor axis in Q and PR is drawn perpendicular to the minor axis. If C is the centre of the ellipse, then CQ*CR =

If the normal at any point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the axes at G and g respectively,then find the raio PG:Pg= (a) a:b(b)a^(2):b^(2)(c)b:a(d)b^(2):a^(2)

If normal at any point P to ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1(a > b) meet the x & y axes at A and B respectively. Such that (PA)/(PB) = 3/4 , then eccentricity of the ellipse is:

If a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose centre is C, meets the major and the minor axes at P and Q respectively then (a^(2))/(CP^(2))+(b^(2))/(CQ^(2)) is equal to

If the normal at a point P on the ellipse of semi axes a, b & centre C cuts the major & minor axes at G & g.show that a^2 (CG)^2 + b^2 (Cg)^2 = (a^2 – b^2)^2. Also prove that CG = e^2 CN, where PN is the ordinate of P.

If C is centre of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the normal at an end of a latusrectum cuts the major axis in G, then CG =

A normal inclined at 45^@ to the axis of the ellipse x^2 /a^2 + y^2 / b^2 = 1 is drawn. It meets the x-axis & the y-axis in P & Q respectively. If C is the centre of the ellipse, show that the area of triangle CPQ is (a^2 - b^2)^2/(2(a^2 +b^2)) sq units

If normal at any point P to the ellipse +(x^(2))/(a^(2))+(y^(2))/(b^(2))=1,a>b meets the axes at M and N so that (PM)/(PN)=(2)/(3), then value of eccentricity e is