Coordinate geometry of the circle

Write down the coordinates of the centre of the circle.

Write down the radius of the circle.

The line $AB$ is a diameter of this circle.
The point $A$ has coordinates $(-1, 6)$.

Find the coordinates of the point $B$.

Show that $A$ lies on the circumference of the circle.

Given that $AB$ is a diameter of the circle, find the coordinates of $B$.

Find the equation of the tangent to the circle at $A$.

Show that the line $y = 2x - 3$ is a tangent to this circle.

Given that this tangent touches the circle at the point $P$, find the coordinates of $P$.

Find the equation of the circle which has its centre at $P$ and passes through the origin.

Find the equation of the circle.

The line $y = 2x + a$, where $a$ is a constant, is also a tangent to the circle.

Show that $5x^2 + 4(a - 2)x + (a - 1)^2 = 0$, and hence find the possible values of $a$.

Give your answers in exact form.