CONK | I GEOMETRICAL. 



486. An ellipse is described touching two confocal ellipses, 

 and having the same centre; prove that the tangents to the two 

 ellipses at two points of contact will be perpendicular to each 

 other. 



487. An ellipse is described having double contact with each 

 of two confocal ellipses ; prove that the sum of the squares on its 

 axes is constant. 



488. If SY, SZ be perpendiculars from the focus S on two 

 tangents drawn from T to a conic, the perpendicular from T on 

 }'Z will pass through the other focus. 



489. The tangent to a conic at P meets the axes in T, t, 

 and the central radius at right angles to CP in <?; prove that QT 

 bears to Qt a constant ratio. 



490. The foot of the perpendicular from the focus of a conic 

 on the tangent at the extremity of the farther latus n-ctuin lies on 

 the minor axis. 



491. The tangents and normals drawn to a series of confocal 

 conies at the extremities of their latera recta will touch two para- 

 bolas having their foci at the given foci and touching each other 



at the centn -. 



492. Through a given point on a given conic are drawn two 

 chords 01\ OQ, equally inclined to a given straight line; prove 

 that PQ passes through a fixed ]n>int. 



493. A chord PQ of a conic is normal at P, and a <lian 

 A// is drawn bisecting the rli..nl ; pr.\\- that J'Q makes c.ju.il 

 angles with /./'. ///'. paid /.'/' N !, (ant. 



'. A given fmitr straight lino is an c< gate dia- 



meter of an ellipse; prove that the locus of ! u 



uiscate. 



495. A parallrlogram is lascri!^! in a <..ni.-, an<l t cm nny 

 point <>n thi.s c-iii<' arc drawn two straight line* each parulh 1 i-> 



