The number of integral values of $k$ for which the line $3x + 4y = k$ intersects the circle $x^{2} + y^{2} - 2x - 4y + 4 = 0$ at two distinct points is

$A$ square is inscribed in the circle $x^2+y^2-2x+4y-93=0$ with its sides parallel to the coordinate axes. Which of the following can be one of the vertices of the square?

If a circle with radius $2.5$ units passes through the points $(2, 3)$ and $(5, 7)$,then its centre is

The number of circles that touch the coordinate axes and the line with slope $-1$ and $y$-intercept $1$ is:

Let the circle with centre at origin pass through the vertices of an equilateral triangle $ABC$. If $A = (2, 4)$,then the length of the median through $A$ is

Let $L_1$ be a straight line passing through the origin and $L_2$ be the straight line $x+y=1$. If the intercepts made by the circle $x^2+y^2-x+3y=0$ on $L_1$ and $L_2$ are equal,then which of the following equations represent $L_1$?