The pair of lines (l x^2+2(l+m) x y+m y^2=0 ) lies along two diameters of a circle and divides the circle into 4 sectors. If the area of bigger sector is 5 times the area of smaller sector, then ( l m (l+m)^2 = )

Step-by-step solution

Let angle between given pair of lines is ' ( ). According to given information, (A₂=5 A₁ 1 2 ( - ) r^2= ( 1 2 r^2 ) 5 ) ( array ll - =5 = 6 6 = l+m (l-m)^2+4(l+m)^2 3 2 = l+m 5 l^2+5 m^2+6 l m 3 4 = (l+m)^2 5 l^2+5 m^2+6 l m 15 l^2+15 m^2+18 l m=4 l^2+4 m^2+8 l m 11 l^2+11 m^2+10 l m=0 11 (l^2+m^2+2 l m )-22 l m+10 l m=0 11(l+m)^2-12 l m=0 l m (l+m)^2 = 11 12 array ) Hence, option (c) is correct.