The length of the intercept that the circle $x^2 + y^2 + 10x - 6y + 9 = 0$ makes on the $x$-axis is:

If the straight lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are the tangents to the same circle,then the area of that circle (in square units) is

Let $A(2,3)$,$B(3,-1)$,and $C(-3,2)$ be three points. If the centre of the circle passing through $A$,$B$,and $C$ is $O(h, k)$,then find the value of $2k - 4h$.

$A$ line meets the coordinate axes at $A(a, 0)$ and $B(0, b)$. If the perpendicular distances from $A$ and $B$ to the tangent drawn at the origin to the circumcircle of $\triangle OAB$ are $m$ and $n$ respectively,then the diameter of that circle is

If the straight line $y=mx$ lies outside of the circle $x^2+y^2-20y+90=0$, then the value of $m$ will satisfy

The centre of the circle passing through the point $(0, 1)$ and touching the curve $y = x^2$ at $(2, 4)$ is