If the shortest distance from $(2,-14)$ to the circle $x^2+y^2+6x+4y-12=0$ is $d$ and the length of the tangent drawn from the same point to the circle is $l$,then $\sqrt{d+l}=$

The equation of the incircle of the triangle formed by the lines $x=0, y=0$ and $3x+4y-24=0$ is

The line $y = mx + c$ intersects the circle $x^2 + y^2 = r^2$ at two real distinct points,if

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

Let $A_0 A_1 A_2 A_3 A_4 A_5$ be a regular hexagon inscribed in a circle of unit radius. The product of the lengths of the line segments $A_0A_1$,$A_1A_2$,and $A_0A_4$ is

Let the equation of the circle,which touches the $x$-axis at the point $(a, 0), a > 0$ and cuts off an intercept of length $b$ on the $y$-axis,be $x^2 + y^2 - \alpha x + \beta y + \gamma = 0$. If the circle lies below the $x$-axis,then the ordered pair $(2a, b^2)$ is equal to: