Prove that the locus of the centre of the circle `(1)/(2)(x^(2)+y^(2))+xcostheta+ysintheta-4=0` is `x^(2)+y^(2)=1`

The locus of the centre of the circle : x^2+y^2+4x cos theta - 2 y sin theta - 10 = 0 is ,

Find the centre of circle 5x^(2)+5y^(2)+4x-8y=16.

Find the centre of the circle x^2+y^2+2x+2=0

Find the centre of the circle 3x^2+3y^2-6x-12y-2=0

Find the centre and radius of the circle 2x^(2)+2y^(2)=3x-5y+7

The length of the common chord of the circle x^(2)+y^(2)+2 x+3 y+1=0 and x^(2)+y^(2)+4 x+3 y+2=0 is

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

If P is a point such that the ratio of the squares of the ltngths of the tangtnts from P to the circleS x^(2)+y^(2)+2 x-4 y-20=0 and x^(2)+y^(2)-4 x+2 y-44=0 is 2: 3, then the locus of P is a circle with centre