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.

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 center of the circle lies on x-2y=4 . Then find the radius 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.

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

Find the equation of a circle passing through the points (-1,5) and (-7,5) and its centre lies on the line 3x+4y+8=0.

If the line y=2-x is tangent to the circle S at the point P(1,1) and circle S is orthogonal to the circle x^2+y^2+2x+2y-2=0 then find the length of tangent drawn from the point (2,2) to the circle S

Obtain the equations of the straight lines passing through the point A(2, 0) & making 45 with the tangent at A to the circle (x + 2)^2 + (y-3)^2 = 25 . Find the equations of the circles each of radius 3 whose centres are on these straight lines at a distance of 5sqrt2 from A.

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 equation of circle with centre (2, 3) and touching the line 3x - 4y + 1 = 0

If the line 4x - 3y = -12 is tangent at point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1) to a circle then equation of circle