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

When do the circles represented by the equations $x^{2} + y^{2} + c^{2} = 2ax$ and $x^{2} + y^{2} + c^{2} = 2by$ touch each other externally?

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

Observe the following statements:
$I$. The circle $x^2+y^2-6x-4y-7=0$ touches the $y$-axis.
$II$. The circle $x^2+y^2+6x+4y-7=0$ touches the $x$-axis.
Which of the following is a correct statement?

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 length of the chord intercepted by the circle $x^2+y^2-4x+6y-12=0$ on the line $4x+3y+1=0$ is