MathematicsChapter 6: Analytical Geometry
Locus and Modelling
Translate a geometric condition into a distance equation, simplify, then interpret the resulting curve.
Learning objectives
- State the rule for locus and modelling.
- Solve a locus and modelling problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Translate a geometric condition into a distance equation, simplify, then interpret the resulting curve.
Formula
x=0.
Where / symbols
- Locus and modelling
- Translate a geometric condition into a distance equation, simplify, then interpret the resulting curve.
CONCEPT AND RULE
Translate a geometric condition into a distance equation, simplify, then interpret the resulting curve.
METHOD
For locus and modelling, 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 equidistant from (2,0),(-2,0) satisfy x=0.
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 locus and modelling
- 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 equidistant from (2,0),(-2,0) satisfy x=0.
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
- Locus and modelling
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Locus and Modelling
Sticky Notes · Formula and Worked Revision
Core Idea
- Translate a geometric condition into a distance equation, simplify, then interpret the resulting curve.
Rule / Formula
- Translate a geometric condition into a distance equation, simplify, then interpret the resulting curve.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- Points equidistant from (2,0),(-2,0) satisfy x=0.
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
- Translate a geometric condition into a distance equation, simplify, then interpret the resulting curve.
- Worked pattern: Points equidistant from (2,0),(-2,0) satisfy x=0.
- Final check: domain, sign, notation, units, and reasonableness.
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