Equation of a Circle (AQA GCSE Further Maths): Exam Questions

A circle, centre $C$, touches the $y$-axis at the point $(0,2)$

The line $y=k$ intersects the circle at the points $(1,k)$ and $(5,k)$

Work out the equation of the circle.

A circle, centre $C$ (4, –2), passes through the origin and point $A(8,0)$ on the $x$-axis.

The tangent at $A$ is shown.

Work out the equation of the circle.

Work out the equation of the tangent to the circle at $A$.

The equations of the two circles shown are

$x^2+y^2=100$and $x^2+y^2=36$

Work out the shaded area. Give your answer as an integer multiple of $\pi$.

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A circle has equation   $x^2+y^2=29$

$P$ is the point $(–5,2)$

Show that $P$ is on the circle.

The tangent to the circle at $P$ intersects the $x$-axis at point $Q$.

Work out the $x$-coordinate of $Q$.

You must show your working.

${\left(x-6\right)}^2+{\left(y-4\right)}^2=25$ is the equation of a circle.

The point $A$ has coordinates $\left(3,8\right)$ and lies on the circle.

The point $B$ lies on the same circle such that $AB$ is a diameter.

The diameter $AB$ lies along a straight line, $l$.

Find the equation of $l$, giving your answer in the form $y=mx+c$.

 A circle has centre $C$and equation ${(x–1)}^2+{(y+3)}^2=25$

$P$$\left(4,–7\right)$ and $Q$ are points on the circle.

The tangent at $Q$ is parallel to the $x$-axis.

The tangents at $P$ and $Q$ intersect at point $R$.

Write down the coordinates of $C$.

Show that the equation of the tangent at $Q$ is $y=2$

Work out the $x$-coordinate of $R$.

The circle with centre $\left(-k,2k\right)$ and radius $\left(3k+1\right)$ goes through the point $\left(1,-4\right)$.

Find the two possible values of $k$.

A tangent touches a circle at the point $\left(-1,8\right)$.

A parallel tangent touches the same circle at the point $\left(3,6\right)$.

Find the equation of the circle.

Give your answer in the form $x^2+y^2+ax+by+c=0$ where $a$, $b$ and $c$ are integers.