The minimum distance and maximum distance of the point $P(2,-7)$ from the circle $x^2+y^2-14x-10y-151=0$ are respectively . . . . . . units.

The number of common tangents to the circles $x^2 + y^2 = 4$ and $x^2 + y^2 - 6x - 8y = 24$ is

When do the two circles $x^2 + y^2 = ax$ and $x^2 + y^2 = c^2$ $(c > 0)$ touch each other?

Let the line $x - y = 4$ intersect the circle $C : (x - 4)^2 + (y + 3)^2 = 9$ at the points $Q$ and $R$. If $P(\alpha, \beta)$ is a point on $C$ such that $PQ = PR$, then $(6\alpha + 8\beta)^2$ is equal to . . . . . .

In a rectangle $ABCD$,the coordinates of $A$ and $B$ are $(1, 2)$ and $(3, 6)$ respectively,and some diameter of the circumscribing circle of $ABCD$ has the equation $2x - y + 4 = 0$. Then,the area of the rectangle is

If the lines joining the origin to the points of intersection of a line $L$ and $x^2+y^2=4$ are the coordinate axes,then the equation of the line $L$ is