The line $x+y+1=0$ intersects the circle $x^2+y^2-4x+2y-4=0$ at the points $A$ and $B$. If $M(a, b)$ is the midpoint of $AB$,then $a-b=$

Find the equation of the director circle of the circle $x^2 + y^2 = 8$.

Given two circles $x^2+y^2+8x-6y-24=0$ and $x^2+y^2-4x+10y+20=0$. Then they are

Let $OA$ be a radius of a circle with center $O$ and radius $d$. Let $B$ be a point on the circle such that $\angle AOB = \theta$ $(< \frac{\pi}{2})$. Let $D$ be a point on $OA$ such that $BD \perp OA$. Let $E$ be the mid-point of $BD$ and $F$ be a point on the arc $AB$ such that $EF \parallel OA$. Then,the ratio of the length of the arc $AF$ to the length of the arc $AB$ is

If two vertices of an equilateral triangle are $(-1, 0)$ and $(1, 0)$,then its circumcircle is:

The condition that the circle $(x - 3)^2 + (y - 4)^2 = r^2$ lies entirely within the circle $x^2 + y^2 = R^2$ is: