TopicFurther Maths
Pure · SS1–SS2
Coordinate geometry & circles
Lines and circles on the coordinate plane: equations, tangents and intersections.
- Before this
- Coordinate geometry
- Leads to
- Conic sections
Learn
- 1Straight linesDistance, midpoint, gradient and the equation of a line; parallel and perpendicular lines, perpendicular bisectors, the angle between two lines, and dividing a line internally or externally.Done20 min
- 2The equation of a circleThe circle with a given centre and radius, reading the centre and radius from the general equation, tangents, circles through three points, and where a line meets a circle.Done20 min
Flashcards
11 cards: the rules, facts and methods to know by heart, with the diagrams from the lessons. They come back until you know them.
Practise
Answer coordinate geometry & circles questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.
Your progress is saved on this device as you practise. No account needed.
Past questions (40)
From 2008–2023: 34 WAEC, 6 NECO. Theory questions first, then objective, newest first.
Theory (28)
- NECO 2023 · Paper 2 · Q12The vectors , and are , …
- NECO 2023 · Paper 2 · Q2Find the equation of the circle whose centre is and which passes through .
- NECO 2023 · Paper 2 · Q9Find the centre and radius of the circle .
- WAEC 2023 · Paper 2 · Q4An equation of a circle is , where is a constant. If the radius of the circle is units, find …
- WAEC 2022 · Paper 2 · Q11Write down the matrix of the linear transformation defined by .
- WAEC 2020 · Paper 2 · Q9Two lines and pass through the point of intersection of and . passes through and …
- WAEC 2019 · Paper 2 · Q2Find the coordinates of the point which divides the line joining and externally in the ratio .
- WAEC 2019 · Paper 2 · Q9The curve and the line intersect at two points. Find the:
- WAEC 2019 · Paper 2 · Q3Find the equation of the circle centre which passes through the -intercept of the line .
- WAEC 2018 · Paper 2 · Q9A circle is drawn through the points , and . Find the:
- WAEC 2018 · Paper 2 · Q10Find the equation of the normal to the curve at the point .
- WAEC 2018 · Paper 2 · Q7Two points and have position vectors and . Find the position …
- WAEC 2018 · Paper 2 · Q4The radius of the circle is . Find the:
- WAEC 2018 · Paper 2 · Q9Points , and are the midpoints of the sides , and respectively of triangle . Find the equation …
- WAEC 2017 · Paper 2 · Q1If and , , find .
- WAEC 2017 · Paper 2 · Q10If , (i) find the values of for which is undefined; (ii) express in partial fractions.
- WAEC 2017 · Paper 2 · Q7A parallelogram has vertices , , and . Find the coordinates of .
- WAEC 2017 · Paper 2 · Q3A line is parallel to . If the line is the perpendicular bisector of the line joining the points and , find its …
- WAEC 2016 · Paper 2 · Q2Given that , and lie on a straight line, find the value of .
- WAEC 2016 · Paper 2 · Q11Without using mathematical tables or a calculator, solve .
- WAEC 2013 · Paper 2 · Q4The line meets the circle at points and , where is in the first quadrant. Find the coordinates …
- WAEC 2012 · Paper 2 · Q11If and are factors of , find the values of and .
- WAEC 2011 · Paper 2 · Q2Find the equation of the line which passes through the point and is perpendicular to the line .
- WAEC 2010 · Paper 2 · Q9Points and lie on a circle. If the line is a tangent to the circle at , find the:
- WAEC 2009 · Paper 2 · Q7The coordinates of the vertices of triangle are , and . If is the foot of the perpendicular from …
- WAEC 2008 · Paper 2 · Q4A straight line passes through the point . Another line which passes through intersects the first line at the point , …
- WAEC 2008 · Paper 2 · Q9The sum of the first terms of a sequence is given by . Write down the first four terms of the sequence …
- WAEC 2008 · Paper 2 · Q10The equation of a circle is , where is a constant. If the radius of the circle is , find the value …
Objective (12)
- NECO 2023 · Paper 1 · Q26Find the distance between the points and .
- NECO 2023 · Paper 1 · Q27Find the equation of the straight line which passes through and .
- NECO 2023 · Paper 1 · Q29Find the equation of the circle which has its centre at and passes through .
- WAEC 2023 · Paper 1 · Q12Given that is the midpoint of and , find the length .
- WAEC 2023 · Paper 1 · Q33Find the radius of the circle .
- WAEC 2022 · Paper 1 · Q29Find, correct to the nearest degree, the acute angle formed by the lines and .
- WAEC 2022 · Paper 1 · Q33The equation of a circle is given as . Find the coordinates of its centre.
- WAEC 2022 · Paper 1 · Q40The length of the line joining points and is 7 units. Find the value of .
- WAEC 2020 · Paper 1 · Q24A circle with centre passes through the point . Find its equation.
- WAEC 2020 · Paper 1 · Q25Calculate, correct to two decimal places, the area enclosed by the line and the axes.
- WAEC 2020 · Paper 1 · Q27Which of the following is not an equation of a circle?
- WAEC 2020 · Paper 1 · Q36 and are two points in a plane. Find the gradient of the line that is normal to the line .