If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

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 of the ellipse , then a^2\ CL^2 + b^2\ CM^2 is equal to (A) (a-b) (B) (a^2 - b^2)^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 .

A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=1 intersects the major and minor axes at points A and B , respectively. If C is the center of the ellipse, then find area of triangle A B Cdot

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 ratio 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 of the ellipse (x^(2))/(16)+(y^(2))/(9) =1 meets the coordinate axes at M and N respectively, then |PM|: |PN| equals

Consider the ellipse whose major and minor axes are x-axis and y-axis, respectively. If phi is the angle between the CP and the normal at point P on the ellipse, and the greatest value tan phi is 3/4 (where C is the centre of the ellipse). Also semi-major axis is 10 units . The eccentricity of the ellipse is

If normal at any poin P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtbgt0) meets the major and minor axes at Q and R, respectively, so that 3PQ=2PR, then find the eccentricity of ellipse

Ifthe normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes in G and g and C is the centre of the hyperbola, then

Find the equation of the ellipse whose foci are at (-2, 4) and (4, 4) and major and minor axes are 10 and 8 respectively. Also, find the eccentricity of the ellipse.