Prove that the centre of the smallest circle passing through origin and whose centre lies on `y = x + 1` is `(-(1)/(2), (1)/(2))`

The area of the circle which passes through the point (4,6) and whose centre is (1,2) is-

The centre of a circle passing through the points (0,0),(1,0)and touching the circle x^2+y^2=9 is

Find the equation of the circle passing through (6, -5) and having centre at (3, -1).

Find the equation of the circle passing through the points (2,3) and (-1,-1) and whose centre is on the line x-3y-11=0.

Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x+y=16 .

The locus of the centre of the circle which passes through the origin and cuts off a length 2b from the line x = c is

Find the equation of the circle, passing through the origin and the foci of the parabolas y^(2) = 8x and x^(2) = 24 y .

Find the equation of the circle which passes through the point (2, -2) and (3, 4) and whose centre lies on the x + y = 2

Find the equation of the circle passes through the points (4,3) and (-2,5) and whose centre lies on the lin 2x-3y=4

Find the equation of the smallest circle passing through the point of intersection of the line x+y=1 and the circle x^(2)+y^(2)=9 .