A circle has radius 3 units and its centre lies on the line y=x-1. Find the equation of the circle if it passes through (7,3).

The line 5x-y=3 is a tangent to a circle at the point (2,7) and its centre is on theline x+2y=19. Find the equation of the circle.

A circle touches both the x-axis and the line 4x-3y+4=0 . Its centre is in the third quadrant and lies on the line x-y-1=0 . Find the equation of the circle.

A circle of radius sqrt8 is passing through origin the point (4,0) . If the centre lies on the line y = x , then the equation of the circle is

Find the equation of the circle of radius 5 cm, whose centre lies on the lies on the y-axis and which passes through the point (3, 2 )

A circle of radius 5 is tangent to the line 4x-3y=18 at M(3,-2) and lies above the line.The equation of the circle is

(i) A circle whoe centre is the point of intersection of the line 2x - 3y + 4 - 0 and 3x + 4y - 5 = 0 passes through the origin. Find its equation. (ii) Find the equation of the circle passing through the point (1,-1) and centre at the intersection of the lines (x -y) = 4 and 2x + 3y = -7.

A circle is drawn with its centre on the line x+y=2 to touch the line 4x-3y+4=0 and pass throughthe point (0,1). Find its equation.

Find the equation of the circle of radius 5 whose centre lies on y-axis and passes through (3,2).