DYNAMICS OF A POINT. 285 



7. A point describes an ellipse with accelerations/^,), 

 <f>(r a ) tending to the foci ; prove that 



r, r t being the focal distances. 



1368. The parabola y'=4ax is described by a point under 

 accelerations A", Y parallel to the axes; prove that 



_ 



dx d 



13G9. A point describes a parabola under acceleration which 

 makes a constant angle a with the normal, is the angle described 

 fn.iu the vertex about the focus in a time t ; prove that 



dO -' 





Find also the law of acceleration. 



1370. A point describes a circle of radius \<i with uniform 

 angular velocity to about the centre, and another point (J d< -M-i-iln-s 

 a eirrle'of radius a with angular velocity 2o> about 1' ; pn\ , 

 tin- I 'ii of Q varies as the distance of P from a certain 



i point. 



1-!71. An equiangular spiral is described by a point with 

 constant acceleration in a d making an angle </> with the 



normal : hat 



d<l> 

 sin < ,T| as 2 sin <f> 4- cot a cos < ; 



a being the constant angle of th<- spiral, and th<- angle through 

 which the tangent hits tmntil from a given position. 



1-"'7L'. 'I 1 re \\hi.li can be described under a con- 



stant acceleration in a <i ing a constant angle with the 



normal is an equiangular spiral. 



