Question

Four distinct points (2k,3k) , (1,0), (0,1) and (0,0) lies on a circle for-

Answer 1

Equation of a circle that contains points `(0,0),(0,1) and (1,0)` is
`x^2+y^2-x-y = 0`
Now, fourth point `(2k,3k)` also lies on this circle,
`:. (2k)^2+(3k)^2-2k-3k = 0`
`=>13k^2-5k = 0`
`=>k(13k-5) =0`
`=> k = 0 and k = 5/13`, which are the required values of `k`.