

41.J //// ION -VJ 



EXAMPLES ON CHAPTER III 

 i and (0,5) on the locus of 3x+2fJ6? 



2. I. lhpoint ;;. " onthk>ctiof 4*<--Of-2 i T 



3. Thfnr.iinate of a certain i-.n.t on the locus of 

 what U iU atcua? What U the urtliimte if the abscissa I* a? 



.1 by the method of Art. 80 whew the following loci eat the axe* 



f x and y. 



4. j.(*-2)(*-3). 5. 



6. jr+0x + y = 4y 



J by the method of Art. 30 where the following loci cut the polar 

 axil (or initial line). 



7 ,. I .*$. a p* = <i' oos '.> 0. 



9. The two loci -*-= 1, + *-=4 intersect in four point*; find 



the length.! of the sides and of the diagonals of the quadrilateral formed 



\>\ til.--,- j-'int*. 



10. A triangle is formed by the point* of intersection of the loci of 

 x + jr = a, x - 2 y = 4 a, and y-x + 7a = 0. Find its area. 



11 1 nd the distance between the point* of intersection of the corvee 

 Jy + 6 = 0, and z* + y = 9. 



12. Does the locus of jr* = 4 * intersect the locus of 2x + 3y + 2 = 0? 

 13 . Does the locus of * - 4 y + 4 = cut the locus of x* + / = 1 ? 



14. For what Tallies of m will the curves x* + y* = 9 and y = 6* + m 

 teneet? (cf. Art. 9.) Trace these curves. 



15 For what value of b will the curves y* = 4 r and y = x + b inter- 

 sect In two distinct points? in two coincident points? in two imaginary 



l-.int.s (,.,-., not intersect)? 



16. 1'iM.l those two values of e for which the points of intersection of 

 the curves y = 2x + c and r* + y = 25 are coincident. 



17 Km. I tli.- . ,ju itioti <if a curve which passes through all the points 

 of inter* ' and y* = 4 r. Test the correctness of the 



result by tin.lui- tli. .-,H, ; ,li!i;itvH of the points of ii 

 stituting them in the equation just found. 



