Show that the equation $x^2+y^2+x-y=0$ represents a circle. Find its centre and radius.

Show that the equation $3x^2+3y^2+6x-4y-1=0$ represents a circle. Find its centre and radius.

Show that the equation $x^2+y^2+2x+10y+26=0$ represents a point circle. Find its centre.

Show that the equation $x^2+y^2-3x+3y+10=0$ does not represent a circle.

Find the equation of the circle passing through the points $(0,0),(5,0) \mathrm{and} (3,3)$. Also, find the centre and radius.

Find the equation of the circle passing through the points $(1,2),(3,-4) \mathrm{and} (5,-6)$. Also, find the centre and radius.

Find the equation of the circle passing through the points $(20,3),(19,8) \mathrm{and} (2,-9)$. Also, find the centre and radius.

Find the equation of the circle which is circumscribed about the triangle whose vertices are $A(-2,3), B(5,2)$ and $C(6,-1)$. Find the centre and radius.

Find the equation of the circle concentric with the circle $x^2+y^2+4x+6y+11=0$ and passing through the point $P(5,4)$.