If the normal at a point P on the ellipse `(x^(2))/(144)+(y^(2))/(16)=1` cuts major and minor axes at Q and R respectively.Then PR:PQ is equal to

The ellipse (x^(2))/(25)+(y^(2))/(16)=1 with the major and minor axis in M and m respectively 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

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 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

For the ellipse 4(x-2y+1)^(2)+9(2x+y+2)^(2)=180 lengths of major and minor axes are respectively

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 ABC.

The tangent and normal at any point P of an ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 cut its major axis in point Q and R respectively. If QR=a prove that the eccentric angle of the point P is given by e^(2)cos^(2)phi+cosphi-1=0

Normal to the ellipse (x^(2))/(64)+(y^(2))/(49)=1 intersects the major and minor axes at PandQ respectively.Find the locus of the point dividing segment PQ in the ratio 2:1.