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

Point of intersection of normal at P(t1) and Q(t2)

Any ordinate MP of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 meets the auxiliary circle at Q. Then locus of the point of intersection of normals at P and Q to the respective curves at x^(2)+y^(2)=8( b) x^(2)+y^(2)=34x^(2)+y^(2)=64 (d) x^(2)+y^(2)=15

P is the point on the ellipse isx^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 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

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 .

Any ordinate MP of an ellipse meets the auxillary circle in Q. Ptove that the locus of the point of intersection of the normals at P and Q is the circle x^(2)+y^(2)=(a+b)^(2) .

The point of intersection of the tangents at the point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and its corresponding point Q on the auxiliary circle meet on the line (a) x=(a)/(e) (b) x=0 (c) y=0 (d) none of these

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 eccentric angles of two points P and Q on the ellipse x^2/a^2+y^2/b^2 are alpha,beta such that alpha +beta=pi/2 , then the locus of the point of intersection of the normals at P and Q is