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.

The line 2x-y+1=0 touches a circle at the point (2, 5) and the centre of the circle lies on x-2y=4 . The diameter (in units) 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 circle lies on x-2y=4. The square of the radius of the circle is

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

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 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.

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

A circle having its centre in the first quadrant touches the y-axis at the point (0,2) and passes through the point (1,0). Find the equation of the circle

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.