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

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

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

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

In an ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 where a gt b , the distance of the normal from the centre does not exceed by ?

P & Q are the corresponding points on a standard ellipse & its auxiliary circle. The tangent at P to the ellipse meets the major axis in T. Prove that QT touches the auxiliary circle.

Equation auxiliary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (a

If normal to x^(2)/a^(2)+y^(2)/b^(2)=1 at any point P meets the major axis is G and PN is perpendicular to the major axis then (CG)/(CN) = (where C is the centre of the ellipse) "

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 .