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 the normal at any point P on the ellipse x^2/64+y^2/36=1 meets the major axis at G_1 and the minor axis at G_2 then the ratio of PG_1 and PG_2 is equal to

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 .

If the normal at P(theta) on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 with focus S ,meets the major axis in G. then SG=

If the normals at P(theta) and Q((pi)/(2)+theta) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meet the major axis at G and g, respectively,then PG^(2)+Qg^(2)=b^(2)(1-e^(2))(2-e)^(2)a^(2)(e^(4)-e^(2)+2)a^(2)(1+e^(2))(2+e^(2))b^(2)(1+e^(2))(2+e^(2))

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

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: