Prove that the points $(6, 9), (0, 1)$ and $(-6, -7)$ are collinear.

Find the value of $h$, if the distance between $(h, 3)$and $(4, 5)$ is $\sqrt{5}$.

Find the value of $k$, if the point $P(0, 2)$ is equidistant from $(3, k)$ and $(k, 5)$.

A line is of length $5$ and one end is at the point $(1, -2)$; if the abscissa of the other end is $4$, prove that its ordinate must be $2$ or $-6$.

Prove that the point $(-1, 2)$ is the centre of a circle passing through the points $(-3, 11), (5, 9), (8, 0)$ and $(6, 8)$. Find the radius of this circle.

Show that the points $A(5, 6), B(1, 5), C(2, 1)$ and $D(6,2)$ are the vertices of a square.

Prove that the points $A(0, 1), B(1, 4), C(4, 3), D(3, 0)$ are the vertices of a square.

If the point $(x, y)$ is equidistant from the point $(a+b, b-a)$ and $(a-b, a+b)$, prove that $bx=ay$.

If the point on $x-$axis, which is equidistant from $(-2,5)$ and $(2,-3)$ is $\left(\mathrm{a},0\right)$, then find the value of $\mathrm{a}$.