A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is :

If 19^th term of a non-zero A.P. is zero, then its (49^th term) : (29^th term) is :

The solution of the differential equation,

$${{dy} \over {dx}}$$ = (x – y)², when y(1) = 1, is :

If  $$\left| {\matrix{ {a - b - c} & {2a} & {2a} \cr {2b} & {b - c - a} & {2b} \cr {2c} & {2c} & {c - a - b} \cr } } \right|$$

      = (a + b + c) (x + a + b + c)², x $$ \ne $$ 0,

then x is equal to :