CONIC SECTIONS, ANALYTICAL. 1 I 1 1 



points, the lines joining which to eitli. r extremity of the major 

 meet the ordinate in /,, M : prove tliat SI* is a harmonic, 

 and NQ a geometric, mean between NL, X M. 



i 



591. On the focal distances of any point of an ellipse as 

 diameters are descriU-d two circles; prove that the eco 

 angle of the point is equal to the angle which a common tangent 

 to the circles makes with the minor axis. 



592. The ordinate NP at a point P of an ellipse is pro- 

 duced to Q, so that XQ : NP :: CA ; CN, and from Q two 

 tangents are drawn to the ellipse ; prove that they intercept on 

 the minor axis produced a length equal to the minor axis. 



593. From a point P of an ellipse two tangents are drawn to 

 the circle on the minor axis; prove that these tangents will meet 

 the diameter at right angles to CP in joints lying on two fixed 

 >t might lines parallel to the major axis. 



1. The lengths of two tangents drawn to an ellipse from a 

 point in one of the equi-conjugate diameters ai < : rove that 



595. AC A' is the major axis, P a point on the auxiliary 

 ; AP t A'P meet the ellipse in Q, <f ; prove that the equation 



/ is 



where is the angle AC P. If an ordinate to P meet Q(f in R, 

 the locus of R is an ellipse to which QQ' is a tangent 



596. A circle is described on a chord of the ellipse lying on 

 the straight line 



that the equation of the line joining the other two points 

 of intersection of the ellipse and circle is 



