CONIC SECTIONS, ANALYTICAL. 



-. From a point are drawn tluve normals OP, OQ, OR, 

 and two tangents OL, J/, to a parabola ; prove that the lata* 

 .OP.OQ.OR 

 OL.OM * 



"73. The normals to the parabola y* = 4ax at points P, Q, J! t 

 meet in the point A. ) ; prove that the co-ordinates of the 

 centre of perpendiculars of the triangle PQR are 



1. A circle and parabola intersect in four points A, B, C, D- 

 AB, CD produced meet in P; BC, AD in Q; both points being 

 without the parabola ; and from any point on the parabola per- 

 pendiculars are let fall on these lines ; prove that the rectangle 

 ined by the perpendiculars on the two former : that con- 

 tained by the perpendiculars on the two latter 



'. In the two parabolas y* = 2c ( *c), a tangent drawn to 

 one meets the other in two points, and on the part intercepted 

 is described a circle ; prove that this circle will touch the second 

 parabola, 



>. On a chord of a given parabola as diameter a circle is 

 led, and the other common chord of the circle and parabola 



is conjugate to the former chord with respect to the parabola; 



prove that each chord will touch a fixed parabola equal to the 



given one. 



577. Two parabolas have a common focus S, and axra in the 

 same straight line, and from a point P on the outer are drawn 

 two tangents PQ, PQf to tin- rove that the ratio 



qpg 



*^r : **~T- 



is constant, A being the vertex of either parabola. 



5, If a parabola circumscribe a triangle ABC, and it* axis 

 make with BG an angle $ (measured from CB towards CA), ita 



w. 8 



