Find the equation of the circle with radius 5 whose center lies on the x-axis and passes through the point (2,3)

If the lines $x+y=6$ and $x+2y=4$ are diameters of the circle which passes through the point (2,6), then find its equation.

Find the equation of circle having centre at (2,3) and touching the line $x+y=1$.

Find the equations of circles each having radius 5 and touching the line $3x+4y-11=0$ at point (1,2).

Find the locus of the midpoint of the chords of circle $x^2+y^2=a^2$ having fixed length l.

Find the locus of midpoint of the chords of the circle $x^2+y^2=a^2$ which subtends a right angle at the point (c,0).

Consider the quadrilateral formed by four lines $3x+4y-5=0,4x-3y-5=0,3x+4y+5=0$ and $4x-3y+5=0$ . Find the equation of the circle inscribed in the quadrilateral and circumscribing the quadrilateral.

A circle touches the line $y=x$ at a point P such that $OP=4\sqrt{2}$. Where O is the origin . The circle contains the point (-10,2) in its interior and the length of its chord on the line $x+y=0$ is $6\sqrt{2}$ . Determine the equation of the circle.

Find the equations of the circles passing through the point (-4,3) and touching the lines $x+y=2$ and $x-y=2$

Find the equation of the circle which is touched by $y=x$, has its centre on the positive direction of the x-axis and cuts off a chord of length 2 units along the line $x=\sqrt{3}y=0$.