Circles Test 2...

ABCD is a square of side 1 unit. A circle passes through vertices A,B of the square and the remaining two vertices of the square lie out side the circle. The length of the tangent draw to the circle from vertex D is 2 units. The radius of the circle is 

Find the equation of the circle having $$(1, -2)$$ as its centre and passing through the intersection of the lines $$3x+y=14$$ and $$2x+5y=18$$.

The equation of the circle which bisects the circumference of the circles  $$x^{2}+y^{2} =1, \;x^{2}+y^{2}-2x =3$$ and $$x^2+y^{2}+2y =3$$ is

The equation of the circle passing through $$(4,6)$$ and having centre $$(1,2)$$ is

The equation $$y = \sqrt{2 - x^2 - y^2} + \sqrt{x^2 + y^2 - 2}$$ represents, where $$x > 0$$

The equation of the circle, passing through the point $$\left(2,8\right)$$, touching the lines $$4x-3y-24=0$$ and $$4x+3y-42=0$$ and having x coordinate of the centre of the circle numerically less then or equal to 8 is

The centre of family of circles cutting the family of circles $$x^2+y^2+4x(\lambda-\dfrac{3}{2})+3y(\lambda-\dfrac{4}{3})-6(\lambda+2)=0$$, lies on 

If $$x=2+3\cos\theta$$ and $$y=1-3\sin\theta$$ represent a circle then the centre and radius is?

The equation $${ x }^{ 2 }+{ y }^{ 2 }+4x+6y+13=0\quad $$ represents 

If $$x ^ { 2 } + y ^ { 2 } - 2 x + 2 a y + a + 3 = 0$$ represents a real circle with non-zero radius, then most appropriate is?