CONIC SECTIONS, ANALYTICAL. 145 



707. The asymptotes of the conic 



h^ic 



will touch the parabola 



708. The equation of the director circle of the conic 



is (V - 1) (x* + y* + 2xy cos <a) + h(x + y cos <o) 



+ k (y + x cos <u) - M cos o> = 0. 



709. A conic is drawn to touch four given straight lines, 

 two of which arc ]>;irallel ; prove that its asymptotes will touch a 

 fixed hyperbola, and that this hyperbola touches the diagonals of 



i;idi ilutcral, formed by the four given straight lines, at their 

 middle points. 



710. If a rectangular hyperbola have double contact with a 

 parabola, the centre of the hyperl>ola and the pole of the chord of 



Met will be equidistant from the directrix of tl. .la. 



711. The area of the ellipse of minimum rrcentririty -which 

 drawn touching two given straight lines at A, k 



from their point of intersection is 



(/* + *' ,)* 



vide (V -I- k 9 ) sin a) - - ! 



(/i f + *' + 2A*co.s 

 if e be the minimum ecccntri 



Vf_ 

 ^ 



Tli'. Four points are roch that ellipses can be described 

 Ji them, and c is the least eccentricity of any such ellipse; 



W. 10 



