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

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 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 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 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)

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

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 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 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 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: