Question

the locus of point whose distances to coordinate axes are in the ratio 3:4 is

Answer 1

let a point on the locus be P(a,b).

=> distance of P from x-axis = b
and, distance of P from y-axis = a

now, according to the question,

b:a = 3:4
=> b/a = 3/4
=> 4b = 3a

now putting (x,y) for (a,b)....
we get the eqn. as...
4y - 3x = 0 ........... ans ..

Answer 2

ratio of a:b=3:4

=a/b=3/4(cross multiplication)

=4a=3b

=(taking a=x and b=y)

=4x=3y

=16x^2=9y^2

=16x^2-9y^2=0

there fore the locus =16x^2-9y^2=0