H T//J: sin.ii'. in it l.'l 



21 Kin.l t h equation of the locu* of a j a move* so as U> be 



al*ay equidinlant from lit, and (3. 2). Show that U 



1) are the vertices of an isosceles triangle. 



22. Kin.l the center and radio, of the circle circumscribed about the 



l), (3, ,,, I. 



23 ally the equu he locus of the vertex of a 



triangle hating iU bate and area constant. 



24. Prove analytically that th<* locus of a point equidistant from two 

 given points ( /,. y . ) /.) is the perpendicular bisector of UM line 



-4 the given point*. 



25. The ban* of a triangle U of length 5, and is given in position; 

 the difference of the squares of the other two sides is 7; find the equa- 



te loons of it* 



26. What lines are represented by the equations : 



> *** = ''; (ft) 14x-5xy-y* = 0; (y) xy = 0? 



27 \\i,it must IK? the value of c in order that the lines 3x + y - 2 = 0. 

 y - 3 a O.and 5x + '2 y + c = Oshall pass through a common point? 



2a By finding the area of the triangle formed by the three points 



> and (a, 2 6), prove that these three points are in a str 

 ve this also by showing that t h- t hn-1 )oint is on the line 



n- ti ..... tii.-i kwo. 



29. Ki.,.1. by th. rn.-thod of Art. 80, the point of intersection of the 



3y + 7=0 and 4x = Oy + 2; and interpret the result 

 by means of Arts. 41 and 60. 



30. Prove by Art. 10 (cf. also Arts. 41 and 00). that the equations of 

 two parallel lines differ only in the constant t 



31. Kind the equations of two lines each drawn through the point 



\ith the axes a triangle whose area is -8. 



32. Kin.l the equation of a lino through the poin' uch that 

 the portion between the axes is divided by the given ]H>int in the ratio 



33. Kind the equation of the perpendicular erected at the middle 

 point of the line joining (5, 2) to the intersection of the two lines 



ll and 9x-2y = M. 



