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.

The auxiliary circle of the ellipse x^(2)/25 + y^(2)/16 = 1

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.

The ratio of the area of triangle inscribed in ellipse x^2/a^2+y^2/b^2=1 to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then, find the eccentricity of the ellipse.

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 Aa n dB are the corresponding points of Pa n dQ on he ellipse, respectively, then find the locus of the midpoint of A Bdot

P and Q trisect the line segment joining the points (2,1) and (5,-8) . If the point P lies on 2x-y+k=0, then find the value of k.

Find the normal to the ellipse (x^2)/(18)+(y^2)/8=1 at point (3, 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

If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) meets the auxiliary circle at point Ra n dQ , then find the points of intersection of tangents to the circle at Qa n dRdot

The line x=t meets the ellipse x^2+(y^2)/9=1 at real and distinct points if and only if. |t| 1 (d) none of these

Let P be any point on a directrix of an ellipse of eccentricity e, S be the corresponding focus, and C the center of the ellipse. The line PC meets the ellipse at A . The angle between at A is alpha . Then alpha is equal to