Exercise 1

The origin lies inside the circle

The length of the tangent to the circle $x^2+y^2+2x-6y-6=0$ from the point $\left(4, 5\right)$ is

The radical axis of the circle $x^2+y^2+2x+2y+1=0$ and $x^2+y^2-10x-6y+14=0$ is

The equation of the circle described on the line joining the points $\left(-2, -1\right)$ and $\left(3, 4\right)$ as diameter is

The length of the tangent from the point $\left(1, -4\right)$ to circle $2x^2+2y^2-3x+7y+9=0$ is

For the circles $x^2+y^2-2x+3y+k=0$ and $x^2+y^2-8x-6y-7=0$ to cut each other orthogonally, the value of $k$ must be

The equation of the tangent to the circle $x^2+y^2+2gx+2fy+c=0$ at origin is

The radical axis of two circles and the line of centres of those circles are