equations of straight lines 3

a)given L1 : x -2y -6 =0sub. y =0 into L1
x -2(0) -6 =0 x =6∴ coordinate of A = (6,0)similarly sub. x= 0 into L1y = -3∴ coordinate of B = (0, -3)the slope of L1 = 1/2since L1 ⊥ L2the slope of L2 = -1/(1/2) = -2by slope -intercept form L2 : y = -2x +(-3) sub. y =0 into L2 we obtain x = -3/2coordinate of C = ( -3/2, 0) b)since △ANO　ａｎｄ　△　ABC are similar (AAA)[area △ANO/area △　ABC] = [AO/AC]^2 = [6/ (6+ 3/2)]^2 =(12/15)^2 = 144/225area △ANO : area △　ABC = 144 : 225the area of quad. CONB : the area of △OAN = 225 -144 : 144 = 81 : 144

the ratio ........= 81 :144