144 BOOK OF MATHEMATICAL PROBLEMS. 



the given point to the similar, concentric, and similarly situated 

 conic through that point. 



703. If e be the eccentricity of the conic 



ax 9 + by' + c + 2a 'y + 2b'x + 2cxy = 0, 

 and w the angle between the axes, 



e* _ (a - b}' sin" o> 4- \(a 4- 6) cos w - 2c'}* 

 1 e* (ab c") sin* <o 



704. The co-ordinates of the focus of the parabola 



Jb 



are given by the equations 

 x y 



and the equation of its directrix is 



as (7i + k cos o>) + y (k + h cos CD) = hk cos o>. 



705. In the parabola 



a tangent is drawn meeting the axes in P, Q ; and perpendiculars 

 are drawn from P, Q to the opposite axes respectively ; prove that 

 the locus of the point of intersection of these perpendiculars is 



x + y cos w y 4- x cos w 

 ~ -- + 2 - . -- = 



cos <o. 



70G. The condition that the straight line - + | = 1 should 



a p 



touch the conic 



