Circles Test 5...

The equation of the circle which touches x-axis at $$(0,0)$$ and touches the line $$3x + 4y-  5 =0$$ is

lf the lines $$2x-3y=5$$ and $$3x-4y=7$$ are two diameters of a circle of radius $$7$$ then the equation of the circle is

A line is at a constant distance $$c$$ from the origin and meets the coordinates axes in $$A$$ and $$B$$. The locus of the centre of the circle passing through $$O, A, B$$ is

The area of a circle centered at $$(1,2)$$ and passing through $$(4,6)$$ is

The equation of the circle passing through the point $$(-1,2)$$ and having two diameters along the pair of lines $$\mathrm{x}^{2}-\mathrm{y}^{2}-4\mathrm{x}+2\mathrm{y}+3=0$$ is

If the equation of the incircle of an equilateral triangle is $${ x }^{ 2 }+{ y }^{ 2 }+4x-6y+4=0$$, then the equation of the circumcircle of the triangle is

The equation of the circle having centre $$(1,\ -2)$$ and passing through the point of intersection of the lines $$3x+y=14$$ and $$2x+5y=18$$ is

The equation of the image of the circle $$x^{2}+y^{2}-6x-4y+12=0$$ by the line mirror $$x+y-1=0$$ is

The equation $$x^{2}+y^{2}-2x+4y+5=0$$ represents 

A straight line is drawn through the centre of the circle $${x}^{2}+{y}^{2}=2ax$$ parallel to $${x}+2y=0$$ and intersecting the circle at $${A}$$ and $${B}$$. Then, the area of $$\Delta A{O}{B}$$ is