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 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 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 the normal at P(asectheta,btantheta) to the hyperbola x^2/a^2-y^2/b^2=1 meets the transverse axis in G then minimum length of PG is

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:

If the normal at any point P on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 meets the auxiliary circle at Q and R such that /_QOR = 90^(@) where O is centre of ellipse, then

If the normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes at G and ga n dC is the center of the hyperbola, then (a) P G=P C (b) Pg=P C (c) P G=Pg (d) Gg=2P C

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

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

The length of perpendicular from the centre to any tangent of the ellipse x^2/a^2 + y^2/b^2 =1 which makes equal angles with the axes, is : (A) a^2 (B) b^2 (C) sqrt(a^2-b^2)/2) (D) sqrt((a^2 + b^2)/2)