坐標幾何

Let $O$ be the origin. If the coordinates of the points $A$ and $B$ are $(6,0)$ and $(0,6)$ respectively, then the coordinates of the in-centre of $\triangle ABO$ are

Consider the circle $x^2+y^2-4x+6y-40=0$. Find the slope of the diameter passing through the point $(1,2)$.

A circle $C$ cuts the $y$-axis at $A$ and $B$. If $AB=8$ and the coordinates of the centre of $C$ are $(-3,5)$, then the equation of $C$ is

In the figure, the length of the line segment joining $A$ and $F$ is

$A(2,5)$ and $B(6,-3)$ are two points. If $P$ is a point lying on the straight line $x=y$ such that $AP=PB$, then the coordinates of $P$ are

In the figure, $ABCD$ is a parallelogram. The coordinates of $B$ are

If the equation of the straight line $L$ is $x-2y+3=0$, then the equation of the straight line passing through the point $(2,-1)$ and perpendicular to $L$ is

In the figure, $O$ is the origin. If the equation of the circle passing through $O$, $A$, $B$ and $C$ is $(x+3)^2+(y-4)^2=25$, then the area of the rectangle $OABC$ is

In the figure, the circle passing through $A(0,8)$ and $B(0,2)$ touches the positive $x$-axis. The equation of the circle is

If $a>0$, $b>0$ and $c<0$, which of the following may represent the graph of the straight line $ax+by+c=0$ ?