Target Exercises

The equation of the radical axis of the circle $2x^2+2y^2+14x-18y+15=0$ and $4x^2+4y^2-3x-y+5=0$, is

The equation of the circle whose diameter is the common chord of the circles ${\left(x-a\right)}^2+y^2=a^2$ and $x^2+{\left(y-b\right)}^2=b^2$ is

The equation of the circle which touches the line $x-y=0$ at the origin and bisects the circumference of the circle $x^2+y^2+2y-3=0$, is

The equation of the circle which passes through the origin and belong to the coaxial system of which the limiting points are $\left(1,2\right)$ and $(4,3)$, is

The equation of the circle through the intersection of the circles $x^2+y^2-8x-2y+7=0$ and $x^2+y^2-4x+10y+8=0$ and that passes through the point $\left(-1,-2\right)$, is

The lengths of the tangents from any point of a fixed circle of coaxial system having equation in the form of $x^2+y^2+2g_{i}x+c=0, i=1, 2, 3$  to another fixed circles of the system are in the ratio 

The radius of the smallest circle which touches the straight line $3x-y=6$ at $\left(1,-3\right)$ and also touches the line $y=x$, is

If the circle $x^2+y^2+2gx+2fy+c=0$ is touched by the line $y=x$ at point $P$ such that $OP=6\sqrt{2}$ units, where $O$ is the origin, then the value of $c$ is