1-J-J AXM.YIK' GJCOMETBT Ca V.69. 



34 A )x>int moves so that the square of its distance from the or 

 equals twice the square of its distance from the x-axis ; timl the equation 

 of its locus. 



35. (iivi-ti i ho four lines 



x-2y + 2 = 0, x + 2y - 2 = 0, 3*-y -3 = and x + y + 6 = 0; 

 these lines intersect each other in six point*; find the equations of ill-- 

 three new lines (diagonals), each of which i.s determined by a pair oi the 



B >ix JM lints of intersection. 



36. Kind the {mints of intersection of the loci : 



(a) pcos0- = a and pcostf - * = a; 

 \ o/ \ O/ 



(ft) p con(0 - ^ = ^ and p = a sin 6. 



If two sides of a triangle are taken as axes, the vertices are (0, 0), 

 ( 'r 0). (0. ft)- Prove analytically that : 



37. the medians of a triangle meet in a point ; 



38. the perpendicular from each vertex to the opposite sides meet 

 in a point; 



39. tho line joining the middle points of two sides of a trian- 

 parallel to the third side. 



40. Show that the equation 56 x + 441 ry - M y 2 - 79 x - 47.y + = 

 represents the bisectors of the angles Iwtween the straight Hues repre- 

 sented by 15 x 2 - IQxy - 48 y a - 2z + 10y-l =0. 



41. Two lines are represented by the equation 



!>> = 0. 



Find the angle between them. 



42. Using the product of a side by half the altitude derive the formula 

 [4] for the area of the triangle whose vertices are at the points (*,, ?/,), 

 (S T // 2 ), and (ly, /,). Wherein is this demonstration more general than 

 -iven in Art. _ 



