CONIC SECTIONS, ANALYTICAL. 



V. Polar Co-ordinates. 



C58. The equation of the normal drawn to the circle r = 2a coe 0, 

 at the point where = a, is 



a sin 2a = r sin (2a - 0). 



659. The equation of the straight line which meets the circle 

 r=2acos0, at the points where = o, = /J, is 



'2a cos a cos /? = r cos (a -f ft - 0). 



660. PSQ is a focal chord of a conic, and a parallel chord 

 AP' through the vertex A meets the latus-rectuui in Q ; prove 

 that the ratio SP.SQ : AP' . AQf is constant. 



CGI. Prove that the equations 



-= cos 0*1 



r 



represent the same conic. If (r, 6) be the coordinates of a point 

 on the locus when the upper sign is taken, what will be its 

 co-ordinates when the lower sign is taken f 



-. A conic is described having a common focus with the 

 - = 1 + cos 0, similar to it, and touching it at the , 



= <x; prove that its latus rectum is ' ,, and that 



the angle between the axes of the two oouics is 



sin a 



'. A ti -i angle ABC has iU angular points on a hyperbola, 

 he centre of its circumscribed circle at a focus of the hyper- 

 prove that sin B sin C= 1, D t C being angular point* on 

 the same branch, and the eccentricity. 



