MathematicsChapter 6: Analytical Geometry
Circle Through Three Points
Substitute three noncollinear points into the general equation and solve D,E,F.
Learning objectives
- State the rule for circle through three points.
- Solve a circle through three points problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Substitute three noncollinear points into the general equation and solve D,E,F.
Where / symbols
- Circle through three points
- Substitute three noncollinear points into the general equation and solve D,E,F.
CONCEPT AND RULE
Substitute three noncollinear points into the general equation and solve D,E,F.
METHOD
For circle through three points, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
Points (1,0),(-1,0),(0,1) lie on x2+y2=1.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve circle through three points
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Worked example
- Worked example:
- Points (1,0),(-1,0),(0,1) lie on x2+y2=1.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Circle through three points
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Circle Through Three Points
Sticky Notes · Formula and Worked Revision
Core Idea
- Substitute three noncollinear points into the general equation and solve D,E,F.
Rule / Formula
- Substitute three noncollinear points into the general equation and solve D,E,F.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- Points (1,0),(-1,0),(0,1) lie on x2+y2=1.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Substitute three noncollinear points into the general equation and solve D,E,F.
- Worked pattern: Points (1,0),(-1,0),(0,1) lie on x^2+y^2=1.
- Final check: domain, sign, notation, units, and reasonableness.
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