If two opposite vertices of a square are $(5, -4)$ and $(-3, 2)$,find its area.

The area of the triangle formed by the lines $y = m_1x + c_1$,$y = m_2x + c_2$ and $x = 0$ is:

$L \equiv 7x - y + 8 = 0$ is one of the diagonals of a square for which $(-4, 5)$ and $(3, 4)$ are two vertices. Find the coordinates of the two vertices lying on the diagonal $L = 0$.

Three points are $A(6, 3)$,$B(-3, 5)$,and $C(4, -2)$. If $P(x, y)$ is a point,then the ratio of the area of $\Delta PBC$ to the area of $\Delta ABC$ is:

$A$ straight line $4x+y-1=0$ passing through the point $A(2,-7)$ meets the line $BC$ whose equation is $3x-4y+1=0$ at the point $B$. Then the equation of the line $AC$ such that $AB=AC$,is

The circumradius of the triangle formed by the lines $xy+2x+2y+4=0$ and $x+y+2=0$ is