Equation of a Circle Practice Questions

The equation of the circle is $x^2 + y^2 = 56.25$.

Write down the radius of the circle.

A different circle has centre the origin and radius $11$.

Write down an equation of this circle.

On the grid, draw the graph of $x^2 + y^2 = 20.25$

Write down the coordinates of the point where $C$ crosses the negative $x$-axis.

Show that the point $A(6, 3)$ lies on $C$.

Determine whether the point $P(5, 4)$ lies inside $C$ or outside $C$.
You must show your working.

The point $Q$ has coordinates $(k, 2k)$ and lies on $C$.

Find the two possible values of $k$.

Write down the radius of $C$.
Give your answer as a surd in its simplest form.

Find an equation of the tangent to $C$ at $P$.
Give your answer in the form $ax + by + c = 0$ where $a$, $b$ and $c$ are integers.

Find the coordinates of $A$ and the coordinates of $B$.

Work out the length of $AB$.
Give your answer in the form $k\sqrt{2}$, where $k$ is an integer.

Draw a sketch of circle $B$.
Label with coordinates the centre of circle $B$ and any points of intersection with the $y$-axis.

Explain why circle $B$ does not cross the $x$-axis.

The circle $C$ has centre the origin $O$ and equation $x^2 + y^2 = 45$
The line with equation $y = 2x$ crosses $C$ at the point $A$, where $A$ lies in the first quadrant.
The tangent to $C$ at $A$ crosses the $x$-axis at the point $T$.

Work out the area of triangle $OAT$.
You must show all your working.