Circles Test 1...

Find the equation of the circle which touches the coordinate axes and whose centre lies on the line $$x - 2y = 3$$.

If $$A(5,-4)$$ and $$B(7,6)$$ are points in a plane, then the set of all points $$P(x,y)$$ in the plane such that $$AP=PB=2:3$$ is

The equation of the circle which passes through the points $$(2, 3)$$ and $$(4. 5)$$ and the centre lies on the straight line $$y - 4x + 3 = 0$$, is

The equation of the image of the circle $${ x }^{ 2 }+{ y }^{ 2 }+16x-24y+183=0$$ by the line mirror $$4x+7y+13=0$$ is:

The equation of the circle, which is the mirror image of the circle, $${ x }^{ 2 }+{ y }^{ 2 }-2x=0$$, in the line, $$y=3-x$$ is:

Point $$\left( 0,\lambda  \right) $$ lies in the interior of circle $$x^2+y^2=c^2$$ then

Statement-1 : The only circle having radius $$\sqrt {10}$$ and a diameter along line $$2x + y=5$$ is $$x^2 + y^2 - 6x + 2y=0$$.
Statement-2: The line 2x + y=5 is a normal to the circle $$x^2+ y^2 - 6x + 2y =0.$$

The equation of the circle passing through $$(4,\ 5)$$ having the centre at $$(2 ,\ 2)$$ is

Find the equation of the circle which passes through the point $$(1, 1)$$ & which touches the $$x^2 + y^2 + 4x - 6y - 3 = 0$$ at the point $$(2, 3)$$ on it.

Find the equation of the circle which passes through the point (1, 1) & which touches the circle $$x^{2} + y^{2} + 4x - 6y - 3 = 0$$ at the point $$(2, 3)$$ on it.