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

The tangent to x^(2)//a^(2)+y^(2)//b^(2)=1 meets the major and minor axes in P and Q respectively, then a^(2)//CP^(2)+b^(2)//CQ^(2)=

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 .

If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts equal lengths l on the axes, then find l .

If a tangent having a slope of -4/3 to the ellipse x^2/18 + y^2/32 = 1 intersects the major and minor axes in points A and B respectively, then the area of DeltaOAB is equal to (A) 12 sq. untis (B) 24 sq. units (C) 48 sq. units (D) 64 sq. units

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

tangent drawn to the ellipse x^2/a^2+y^2/b^2=1 at point 'P' meets the coordinate axes at points A and B respectively.Locus of mid-point of segment AB is

If the normal at point P (theta) on the ellipse x^2/a^2 + y^2/b^2 = 1 meets the axes of x and y at M and N respectively, show that PM : PN = b^2 : a^2 .

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 Ga n dg, respectively, then P G^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)

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