A circle is tangent to line 3x-4y+1=0 at (1,1) and is normal to line 2x+y-5=0 .then find the equation of circle

The line 2x-3y+1=0 is tangent to a circle S=0 at (1,1). If the radius of the circle is sqrt(13). Find theequation of the circle S.

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.

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.

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

If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle,then find the radius of the circle.

If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle,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 center of the circle lies on x-2y=4. Then find the radius of the circle.

The foot of the normal from the point (1,2) to a circle is (3,4) and a diameter of the circle has the equation 2x+y+5=0 ,then the equation of the circle is

Find the equation of circle touching the line 2x + 3y + 1=0 at the point ( 1,-1) and is orthogonal to the circle which has the line segment having end poitns (0,-1) and (-2,3) as the diameter.