ANSWERS. 231 



(9) (a) Ellipse; (b) hyperbola; (c) parabola. 

 (10) Parabola : x x^= (y y ) ^L^L {y j ) 2 , where 2 a is the 



distance of <9 3 from the point O that bisects <9i O 2 ; the point midway 

 between O and O 3 is taken as origin, and OO 3 as axis of x. 



(n) /ssItan-f 



/ 



Pages 76, 77. 



(4) 687 days. 



(5) By (24), Art. 138, v* ^ - T - ; as the velocity is not changed 



instantaneously, we must have T - = T , whence the new 



r a r a' 



major semi-axis a' can be found. 



(6) An ellipse with the end of its minor axis at the point where the 

 change takes place. 



(7) (a) Ellipse with a = ^r\ (&) parabola. 



(8) Differentiate (24), Art. 138, with respect to /u, and a. 



(9) The periodic time T would be diminished by T. 



m 



, ^ i ,.,.-. 



(10) r = - ; hence x = - -, y = - ; differ- 

 i + e cos i + e cos i + e cos 



entiating and remembering that rY/0/^= c, we find 

 dx c . /i dy c 



eliminating 0, we find the equation of the hodograph 



_^' = , or since , = 

 (n) 1.016 914. 

 (12) /=JI? 



