80 ANALYTIC GEOMETi: Y [Cn. IV. 49. 



13. Solve example 12 if the word "sum" is substituted for <! 



14. Let M = (o,0), B=(6,0), and -4 ' = (-0, 0) be three fixed points, 

 liml tin- fquation of the locus of the point / > = (r.//) \\hirh moves so 

 i hat I* It* /M t = 2/M*. 



15. A point moves so that \ of its abscissa exceeds | of its ord i 



i \ 1 . i'iii.1 (lie equation of its locus and trace the curve. 



16. Find the equation of the locus of a point that is always equi- 

 :.t from the points (-3,4) and (5, 3); from the poii l ) and 



Hy means of these two equations find the coordinates of the 

 point that is equidistant from the three given points. 



17. Let A = (-l, 3), 5=(-3, -3) C = (l, 2), 7> = (2, 2) be four 

 fixed points, and let P=(x, y) be a point that moves subject to the nm- 

 dition that the triangles PAB and PCD are always equal in area; find 

 the equation of the locus of P. 



18. If the area of a triangle is 25 and two of its vertices are (5, ~6) 

 and ( 3, 4), find the equation of the locus of the third vertex. 



19. A j)oint moves so that its distance from the pole is numerically 

 equal to the tangent of the angle which the straight line joining it to the 

 origin makes with the initial line. I'ind the polar equation of its locus 

 and plot the figure. 



