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 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

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 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)

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 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:

The distance of the point 'theta' on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 from a focus, 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

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

A tangent to the ellipse x^2+4y^2=4 meets the ellipse x^2+2y^2=6 at P&Q.