Hello dear,

Given equation is 3x^2-4xy=0

x(3x-4y) =0

separate equations of the lines are x = 0 and 3x-4y =0

let m1 and m2 be the slopes of these lines

then m1 does not exist and m2 =3/4

now, required lines are perpendicular to these lines

their slopes are -1/m1 and -1/m2

since m1 does not exist -1/m1 =0

also , m2 = 3/4 , -1/m2 =-4/3

Their combined equation is 4xy +3y^2 =0