If the circles $(x+a)^2+(y+b)^2=a^2$ and $(x+c)^2+(y+d)^2=d^2$ cut orthogonally,then $b(b-2d) =$

$A$ circle with radius $12$ lies in the first quadrant and touches both the axes. Another circle has its centre at $(8, 9)$ and radius $7$. Which of the following statements is true?

If $(m_i, \frac{1}{m_i}), i = 1, 2, 3, 4$ are concyclic points,then the value of $m_1 \cdot m_2 \cdot m_3 \cdot m_4$ is

Let $P$ and $Q$ be two distinct points on a circle which has center at $C(2,3)$ and which passes through the origin $O(0,0)$. If $OC$ is perpendicular to both the line segments $CP$ and $CQ$,then the set $\{P, Q\}$ is equal to:

$A$ 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 $.............$.

Match the statements in Column $I$ with the properties in Column $II$.

Column $I$	Column $II$
$(A)$ Two intersecting circles	$(p)$ have a common tangent
$(B)$ Two mutually external circles	$(q)$ have a common normal
$(C)$ Two circles,one strictly inside the other	$(r)$ do not have a common tangent
$(D)$ Two branches of a hyperbola	$(s)$ do not have a common normal