////: n.i.U'SK 



9. The minor axis of .1, ellipse is , and the turn of the focal radii 

 lor a curtain point on the curve U 16; And iu major axis, distance 

 between foci, and area. 



10. A line of fixed length moves to thai IU ends remain in the 

 eoordinate axes; find the loom generated by any point of tho line. 



11 :.,| the locus of the middle poinU of chord* of an ellipse drawn 

 through the positive tad of the minor axU. 



12 With a given focus and directrix a atria* of ellipses are drawn ; 

 bow that the locui of the extremities of Uu-ir minor axes U a parabola. 



13 SliowtbattheUnexooaa + yiinasptoucbeetbeeUipee 



nd the locus of the foot of the perpendicular drawn from the 

 of the ellipse ~ + as 1 to a variable tangent. 



13. Prove, analytically, that if the normals to an ellipse paas through 

 its center, the ellipse is a circle. 



16. Find the locus of the vertex of a triangle of baae 2 a, and such 



the product of the tangents of the angles at its base is - 



17. The ratio of the subnormals for corresponding points on the 

 ellipse and major auxiliary circle is Z. 



18 Fin.l the equation of the ellipse 9r + 25y = 225 when referred 

 to its equi-con jugate diameters. 



19. \ormals at corresponding points on the ellipse, and on the major 

 .try circle, meet on the circle r* + y 1 = (a + 6)*. 



20. Two tangents to an ellipse are perpendicular to each other; find 

 the locos of the middle point of their chord of contact 



21. If P, U a point on the director circle, the product of the distances 

 of the center and the pole, respectively, front iu polar with respect to 

 the ellipse is constant 



The tangents drawn from the point /' to an elliptw make angles e\ 

 ai>.l 0. with the major axi* ; tin. I the locus of /' 



22 \\ lien 0, + 0, = 2 a, a constant 



23 when tan 0, + tan $ t = e, a constant 



