# Exam-Style Questions on Circle Equations

## Problems on Circle Equations adapted from questions set in previous exams.

### 1.

GCSE Higher

The diagram shows a circle with equation $$x^2+y^2=13$$.

A tangent to the circle touches the circle at the point J. The x-coordinate of J is 2. The tangent intersects the x-axis at K. Find the coordinates of the point K.

### 2.

GCSE Higher

(a) Find the coordinates of the point at which the curve $$y = k^x$$ intersects the y-axis.

The equation of circle $$A$$ is $$x^2+y^2=25$$. This circle is translated by the vector $$\begin{pmatrix} 0 \\ 4 \\ \end{pmatrix}$$ to give circle $$B$$.

(b) Draw a sketch of circle $$B$$ clearly labelling the points of intersection with the y-axis.

### 3.

GCSE Higher

A circle with equation $$x^2 + y^2 = 6$$ meets a one of its tangents at point $$S$$.

The coordinates of $$S$$ are:

$$\left( \frac{\sqrt 5}{3} , \frac{7}{3} \right)$$

Find the equation of the tangent to the circle at the point $$S$$.

### 4.

GCSE Higher

(a) The circumference of a circle is $$16 \pi$$ cm and its centre is at the origin. Find the equation of the circle.

(b) The line $$12x+ ay = b$$ is a tangent at the point (6, 5) to a different circle with centre at the origin. Find the values of a and b.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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