Given two points $A(3, 4)$ and $B(5, -2)$. If $PA = PB$ and the area of $\Delta PAB = 10$ square units,find the coordinates of point $P$.

Let the area of the triangle with vertices $A(1, \alpha)$,$B(\alpha, 0)$,and $C(0, \alpha)$ be $4 \text{ sq. units}$. If the points $(\alpha, -\alpha)$,$(-\alpha, \alpha)$,and $(\alpha^2, \beta)$ are collinear,then $\beta$ is equal to:

Let $ABCD$ be a trapezium,in which $AB$ is parallel to $CD$,$AB=11$,$BC=4$,$CD=6$ and $DA=3$. The distance between $AB$ and $CD$ is

Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line $2x + y = 5$. Then the area of the triangle is:

If the vertices of a triangle are $(0, 4)$,$(4, 1)$,and $(7, 5)$,find its perimeter.

If the incentre and the circumcentre of the triangle formed by the lines $x=2$,$4x+3y+7=0$ and $y=3$ are $I$ and $S$ respectively,then $IS=$