Transum Software

Exam-Style Questions on Circle Equations

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

1.

GCSE Higher

The diagram shows a circle with equation \(x^2+y^2=13\).

Diagram

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.


If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.

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.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

 

Exam-Style Questions Main Page

 

Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.

Comments:

Apple

©1997-2024 WWW.TRANSUM.ORG