290 BOOK OF MATHEMATICAL PROBLEMS. 



rip 



point P of the parabola varies as , + ^ 3 , A being the vertex 

 and S the focus. 



1392. The force tending to the pole under which the evolute 

 of the curve rf(p) can be described will vary as 



1393. An orbit described under a constant force tending to 

 a fixed point will be the pedal of one of the curves represented by 

 the equation 



1394. A particle is projected from a point A at right angles 

 to a straight line SA, and attracted to S by a force varying as 

 cosec PSA prove that the rate of describing areas about A will 

 be uniformly accelerated. 



1395. A particle is projected at a distance a with velocity 

 equal to that in a circle at the same distance and at an angle 45 

 with the distance, and attracted to a fixed point by a force which 



(Q 2\ 



-a + J : determine the orbit de- 



scribed, and prove that the time to the centre of force is 



139G. A particle is attracted to a fixed point by a force 

 which at a distance r is equal to 



and is projected from a point at a distance a from the centre with 

 velocity equal to that in a circle at the game distance and in 



