Circles Test 2...

The equation of the circle, the end points of whose diameter are the centre of the circles $$x^{2}+y^{2}+6x-14y=1$$ and $$x^{2}+y^{2}-4x+10y=2$$ is 

The equation of a circle with centre at $$(2,-3)$$ and the circumference is $$10 \pi$$ units is 

Equation having circle centre $$(5, 2)$$ and which passes through the point $$(1, -1)$$ is 

The parametric equation of the circle $$x^{2}+y^{2}+x+\sqrt {3}y=0$$ are

If two vertices of an equilateral triangle are $$A (-a, 0)$$ and $$B(a, 0), a > 0$$ and the third vertex C lies above x-axis then the equation of the circumcircle of $$\Delta ABC$$ is

The equation of the circle of radius $$5$$ with centre on  x-axis and passing through the point $$(2,3)$$ is

The equation(s) of the circle(s) which pass through the ends of the common chords of two circles $$2x^{2}+2y^{2}+8x+4y-7=0$$ and $$x^{2}+y^{2}-8x-4y-5=0$$ and touch the line $$x=7$$ is (are) :

The equation of the circle which touches the axes of $$y$$ at the origin and passing through $$(3,4)$$ is

The equation of the circle with centre at $$(4, 3)$$ and touching the line $$5x-12y-10=0$$ is?

Equation of circle touching the line $$x + y = 4$$ at $$( 1, 3)$$ and intersecting the circle $${ x }^{ 2 }+{ y }^{ 2 }=4$$ orthogonally is