P and Q are corresponding points on the ellipse `x^(2)/a^(2) + y^(2)/b^(2) = 1` and the auxiliary circle respectively . The normal at P to the elliopse meets CQ at R. where C is the centre of the ellipse Prove that CR = a +b

P_(1) and P_(2) are corresponding points on the ellipse (x^(2))/(16)+(y^(2))/(9)=1 and its auxiliary circle respectively. If the normal at P_(1) to the ellipse meets OP_(2) in Q (where O is the origin), then the length of OQ is equal to

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

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

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 =

The locus of points whose polars with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 are at a distance d from the centre of the ellipse, is

If C is centre of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the normal at an end of a latusrectum cuts the major axis in G, then CG =

Prove that area common to ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and its auxiliary circle x^2+y^2=a^2 is equal to the area of another ellipse of semi-axis a and a-b.

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 P(theta),Q(theta+pi/2) are two points on the ellipse x^2/a^2+y^2/b^2=1 and α is the angle between normals at P and Q, then

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 .