Which of the following lines is a diameter of the circle $x^2 + y^2 - 6x - 8y - 9 = 0$?

The number of circles that touch all the straight lines $x+y=4$,$x-y=-2$,and $y=2$ is

Consider a circle $C_1: x^2+y^2-4x-2y=\alpha-5$. Let its mirror image in the line $y=2x+1$ be another circle $C_2: 5x^2+5y^2-10fx-10gy+36=0$. Let $r$ be the radius of $C_2$. Then $\alpha+r$ is equal to $......$.

$ABC$ is a triangle and the radical centre of the circles with $AB, BC, CA$ as the diameters is $(-6,5)$. If $A=(3,2)$ and $B=(2,1)$,then $C=$

The area of a circle whose centre is $(h, k)$ and radius $a$ is

$A$ line $l$ meets the circle $x^2+y^2=61$ at points $A$ and $B$. If $P(-5, 6)$ is a point such that $PA=PB=10$,then the equation of line $l$ is: