If the circle $x^2 + y^2 - 6x - 8y + (25 - a^2) = 0$ touches the $x$-axis,then $a$ equals

The length of the chord joining points $(4 \cos \theta, 4 \sin \theta)$ and $(4 \cos (\theta+60^{\circ}), 4 \sin (\theta+60^{\circ}))$ on the circle $x^2+y^2=16$ is

$A$ circle passing through the point $P(\alpha, \beta)$ in the first quadrant touches the two coordinate axes at the points $A$ and $B$. The point $P$ is above the line $AB$. The point $Q$ on the line segment $AB$ is the foot of the perpendicular from $P$ on $AB$. If $PQ$ is equal to $11$ units,then the value of $\alpha \beta$ is $.............$.

Let $y=x+2$,$4y=3x+6$,and $3y=4x+1$ be three tangent lines to the circle $(x-h)^2+(y-k)^2=r^2$. Then $h+k$ is equal to:

The area of the circle whose centre is at $(1, 2)$ and which passes through the point $(4, 6)$ is

Position of the point $(1, 1)$ with respect to the circle $x^2 + y^2 - x + y - 1 = 0$ is