CONIC SECTIONS, ANALYTICAL. 1 _':; 



602. The three points whose eccentric angles are a, ft y are 

 the angular points of a triangle; prove that the co-ordinates of the 

 centre of perpendiculars of this triangle are 



a'-6* 



and of the centre of the circle circumscribing the triangle are 

 -^- {cosa + cos0 + cosy+oos(a-f + y)}, 



-^- {sin a + sin /? + sin y - sin (a 4- ft + y)}. 



Find the loci of each of these points when the triangle is a 

 maximum, 



603. If a chord of a parabola be drawn through a fixed 

 point on the axis, and an ellipse be described with the extremi- 

 ties of this chord for foci, and passing through the focus of the 

 parabola ; the minor axis of this ellipse will be constant 



604. Two tangents to a given circle intersect a constant 

 length on a fixed tangent ; prove that the locus of their point 

 of intersection is a conic which the given circle osculates at a 

 vertex. 



605. If a tangent be drawn to an ellipse, and with the point 

 of contact as centre another ellipse be described similar and 

 similarly situated to the former, but of three times the area ; then 

 if from any point of this latter ellipse two other tangents be 

 drawn to the former, the triangle formed by the three UngenU 

 will be double of the triangle formed by joining their potato 

 of contact 



606. TV', TQ are tangenti to an ellipse at points whose 

 eccentric angles are a, ft another tangent meets them in P, <f ; 

 prove that 



