The circle $x^2 + y^2 = 4x + 8y + 5$ intersects the line $3x - 4y = m$ at two distinct points if:

$A$ point inside the circle $x^2 + y^2 + 3x - 3y + 2 = 0$ is

Let $C: x^2+y^2=4$ and $C^{\prime}: x^2+y^2-4 \lambda x+9=0$ be two circles. If the set of all values of $\lambda$ such that the circles $C$ and $C^{\prime}$ intersect at two distinct points is $\mathbb{R}-[a, b]$,then the point $(8a+12, 16b-20)$ lies on the curve:

If the power of a point $(4, 2)$ with respect to the circle $x^2 + y^2 - 2\alpha x + 6y + \alpha^2 - 16 = 0$ is $9$,then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is:

If the circle $x^2 + y^2 = a^2$ cuts a chord of length $2b$ on the line $y = mx + c$,then:

If the inverse point of the point $P(3, 3)$ with respect to the circle $x^2+y^2-4x+4y+4=0$ is $Q(a, b)$,then $a+5b=$