Circles Test 1...

The equation of circle with centre $$(1,2)$$ and tangent $$x+y-5=0$$ is

The circle $${x^2} + {y^2} - 3x - 4y + 2 = 0$$ cuts $$x$$-axis

Equation of the circle which passes through the centre of the circle $$x^{2} + y^{2} + 8x + 10y - 7 = 0$$ and is concentric with the circle $$2x^{2} + 2y^{2} - 8x - 12y - 9 = 10$$ is

Equation of the circle of radius 5 whose centre lies on y-axis in first quadrant and passes through$$\left( {3,\,\,\,\,2} \right)$$ is 

The axes are translated so that the new equation of the circle $$x^{2}+y^{2}-5x+2y-5=0$$ has no first degree terms. Then the new equation is

A circle is concentric with circle $$x^{2}+ y^{2}-2x+4y-20=0$$. If perimeter of the semicircle is $$36$$ then the equation of the circle is :

The name of the conic represent by the equation $$x^2+y^2-2y+20x+10=0$$ is

The equation of the circle passing through the foci of the ellipes  $${\frac{x}{{16}}^2} + {\frac{y}{{{9^{}}}}^2} = 1$$ and having centre at $$\left( {0,3} \right)$$ is 

A variable circle is drawn to touch the x-axis at the origin.The locus of the pole at the straight line $$6 x + m y + n = 0$$ w.r.t. the variable circle has the equation:-

Equation of circles which touch both the axes and whose centres are at a distance of $$2\sqrt {2}$$ units from origin are