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 length of the tangent drawn from the point $(2, 3)$ to the circle $2(x^2 + y^2) - 7x + 9y - 11 = 0$ is:

Two circles $x^2 + y^2 = ax$ and $x^2 + y^2 = c^2$ touch each other if:

For the circle $x^2 + y^2 - 2x + 4y - 4 = 0$,what is the line $2x - y - 1 = 0$?

The equation of the circle which touches the coordinate axes and the line $\frac{x}{3} + \frac{y}{4} = 1$,and whose centre lies in the first quadrant,is ${x^2} + {y^2} - 2cx - 2cy + {c^2} = 0$,where $c$ is:

If $(1,3)$ is the midpoint of a chord of the circle $x^2+y^2-4x-8y+16=0$,then the area of the triangle formed by that chord with the coordinate axes is