P is the point on the ellipse is`x^2/16+y^2/9=1 and Q` is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

P is a point on the ellipse x^2/(25)+y^2/(9) and Q is corresponding point of P on its auxiliary circle. Then the locus of point of intersection of normals at P" & "Q to the respective curves is

P is a point on the ellipse E:x^2/a^2+y^2/b^2=1 and P' be the corresponding point on the auxiliary circle C: x^2+y^2=a^2 . The normal at P to E and at P' to C intersect on circle whose radius is

The ratio of ordinates of a point on ellipse and its corresponding point on auxiliary circle is (2sqrt(2))/(3) then its eccentricity is

If the ratio of the ordinate of a point on ellipse and its corresponding point on auxiliary circle is (2sqrt(2))/(3) then its eccentricity is

P is any point on the auxililary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and Q is its corresponding point on the ellipse. Find the locus of the point which divides PQ in the ratio of 1:2 .

Find the points on the ellipse (x^(2))/(4)+(y^(2))/(9)=1 on which the normals are parallel to the line 2x-y=1.

Q is a point on the auxiliary circle of an ellipse. P is the corresponding point on ellipse. N is the foot of perpendicular from focus S, to the tangent of auxiliary circle at Q. Then

Q is the point on the auxiliary circle corresponding to P on the ellipse; PLM is drawn parallel to CQ to meet the axes in L and M prove that PL=b and PN=a

From any point on the line y=x+4 tangents are drawn to the auxiliary circle of the ellipse x^(2)+4y^(2)=4. If P and Q are the points of contact and A and B are the corresponding points of P and Q on he ellipse,respectively,then find the locus of the midpoint of AB.