Circles Test 1...

A circle of radius $$\sqrt 8$$ is passing through origin and the point $$(4, 0)$$. If the centre lies on the line $$y = x$$, then the equation of the circle is

The equation of the circle having $$x-y-2=0$$ and $$x-y+2=0$$ as two tangents and $$x-y=0$$ as diameter is

The lines $$y=x+\sqrt { 2 } $$ and $$y=x-2\sqrt { 2 } $$ are the tangent of certain circle. If the point $$\left( 0,\sqrt { 2 }  \right) $$ lies on this circle, then its equation is

The lines $$2x-3y=5$$ and $$3x-4y=7$$ are the diameters of a circle of area $$154$$ sq.units. The equation of the circle is

The equation of the circle which touches the lines $$x = 0, y = 0$$ and $$4x + 3y = 12$$ is

The radius of the circle passing through the points $$(2,3),(2,7)$$ and $$(5,3)$$ is

The equation of the circumcircle of the triangle formed by the lines $$y + \sqrt{3} x = 6, y - \sqrt{3} x = 6$$ and $$y=0$$ is 

The equation of the circle whose two diameters are the lines $$x+y=4$$ and $$x-y=2$$ and which passes through $$(4 , 6 )$$ is 

If the lines $$3x - 4y - 7 = 0$$ and $$2s - 3y - 5 = 0$$ are two diameters of a circle of area $$49\pi$$ square units, the equation of the circle is-

The equation of the circle passing through $$(2,0)$$ and $$(0,4)$$ and having the minimum radius is