$A$ square is inscribed in the circle $x^2 + y^2 - 2x + 4y + 3 = 0$,whose sides are parallel to the coordinate axes. One vertex of the square is

If the radical axis of the circles $x^2 + y^2 - 1 = 0$ and $x^2 + y^2 - 2x - 2y + 1 = 0$ forms a triangle of area $A$ with the coordinate axes,then the value of $\frac{1}{A}$ is

The area of a circle having the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as two of its tangents is:

$A$ point $P$ is taken outside $\Delta ABC$ where $B(1, \sqrt{3})$,$A(0, 0)$,and $C(2, 0)$,but inside the acute angle $BAC$,such that $\angle APC = \frac{\pi}{6}$ and $\angle BPA = \frac{\pi}{12}$. The slope of the line $BP$ is:

The number of circles that touch all the three lines $x+y-1=0$,$x-y-1=0$,and $y+1=0$ is

If the length of the chord $2x+3y+k=0$ of the circle $x^2+y^2-6x-8y+9=0$ is $2\sqrt{3}$,then one of the values of $k$ is