Let $R$ be a rectangle,$C$ be a circle,and $T$ be a triangle in the plane. The maximum possible number of points common to the perimeters of $R, C$ and $T$ is

$A$ line is drawn through a fixed point $P(\alpha, \beta)$ to cut the circle $x^{2}+y^{2}=r^{2}$ at $A$ and $B$. Then $PA \cdot PB$ is equal to

If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ touches the $x$-axis,then:

If the line $y = mx + 1$ meets the circle $x^2 + y^2 + 3x = 0$ in two points equidistant from and on opposite sides of the $x$-axis,then

If $(6, -k)$ and $(-3, 2)$ are conjugate points with respect to the circle $x^2 + y^2 + 6x + 4y + 12 = 0$,then $k$ equals:

$A$ rectangle is inscribed in a circle with a diameter lying along the line $3y = x + 7$. If the two adjacent vertices of the rectangle are $(-8, 5)$ and $(6, 5)$,then the area of the rectangle (in $sq. units$) is