Which of the following equations represent a circle and if so, find its centre and radius:
`2x^2 + 2y^2 = 5 x + 7y + 3`.

Find the equations of the following curves in cartesian form. Wherever the curve is a circle, find its centre and radius : x= at^2, y=2at .

Find the centre and radius of the circle : 2x^2 + 2y^2- x=0 .

Which of the following equations are consistent? If consistent, find the solutions: {:(2x + 3y = 5),(3x + 2y = 2):}

Find the equations of the following curves in cartesian form. Wherever the curve is a circle, find its centre and radius : x= 1/2 t+1, y= 2t-1 .

Find the equations of the following curves in cartesian form. Wherever the curve is a circle, find its centre and radius : x=5+3 cos alpha, y=7+3 sin alpha .

Prove that the equation x^2 + y^2 + 2gx + 2fy + c = 0 represents a circle and find its centre and radius.

Find the centre and radius of the circle : x^2 + y^2+ 8x + 10y- 8 =0 .

Find the equations of the following curves in cartesian form. Wherever the curve is a circle, find its centre and radius : x=1+2 cos alpha, y=3+2 sin alpha .