Let `u=a x+b y+a ^3sqrt(b)=0,v=b x-a y+b^3sqrt(a)=0,a ,b in R ,` be two straight lines. The equations of the bisectors of the angle formed by `k_1u-k_2v=0` and `k_1u+k_2v=0` , for nonzero and real `k_1` and `k_2` are

Options

A. u=0
B. `k_(2)u + k_(1)v = 0`
C. `k_(2)u - k_(1)v = 0`
D. v=0

Answer

A,D

Explanation

Note that the lines are perpendicular, Assume the coordinates axes to be directed along u=0 and v = 0, Now, the lines `k_(1) u-k_(2)v=0 " and " k_(1) u + k_(2)v =0` are equally inclined with the u-v axes. Hence, the bisectors are u=0 and v=0.