On which line does the centre of the circle lie? `x+y=0`

Consider a circle passing through the origin and the points (a,b) and (-b,-a). On which line does the centre of the circle lie? What is the sum of the squares of the intercepts cut-off by the circle on the axes?

The line 2x-y+1=0 is tangent to the circle at the point (2,5) and the centre of the circles lies on x-2y=4 The radius of the circle is:

The line 2x-y+1=0 is tangent to the circle at the point (2,5) and the centre of the circles lies on x-2y=4. The radius of the circle is

The line 2x - y + 1 = 0 is tangent to the circle at the point (2,5) and the centre of the circles lies on x-2y = 4. The radius of the circle is :

The line 2x-y+1=0 is tangent to the circle at the point (2,5) and the centre of the circles lies on x-2y=4. The radius of the circle is :

Find the equation of the straight line which passes through the centre of the circle x^(2) + y^(2) + 2x + 2y- 23 = 0 and is perpendicular to the straight line x-y+8 = 0.

If the line 2x-y+1=0 touches the circle at the point (2,5) and the centre of the circle lies in the line x+y-9=0. Find the equation of the circle.

If the line 2x-y+1=0 touches the circle at the point (2,5) and the centre of the circle lies in the line x+y-9=0. Find the equation of the circle.

Find the locus of the centre of the circle touching the line x+2y=0a n d x=2y