The equation of a circle and two circles
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 4 worked examples, 6 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Every point the same distance away
- The equation
Read the transcript of the teaching part
Last time
Before we start: last time, in Straight lines, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Every point the same distance away
A circle is all the points the same distance from a centre. Write that sentence in coordinates and you get the equation of the circle. Two circles then give two equations, and the line where they cross is found by subtracting.
The equation
A circle with centre a, b and radius r has equation: x minus a, squared, plus y minus b, squared, equals r squared. Read off the centre from the brackets, but flip the signs. x plus two means a is minus two. The right side is r squared, not r. A common slip.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Line meeting a circle.
The whole chapter: Coordinate Geometry.
Chapter 1.3: Coordinate geometry
- Straight lines: mid-points, equations and straight-line form 6 min
- The equation of a circle and two circles 6 min
- Tangents to a circle and a line and a circle 6 min
Also for A Level Maths 9709 Paper 1
Which topics come up most in A Level Maths 9709 Paper 1 past papers, counted from every paper since 2004.