Locus Problems
Sets of points satisfying a geometric condition.
Key idea
Sets of points satisfying a geometric condition.
In depth
A locus is the set of all points satisfying a condition. The locus equidistant from two points is their perpendicular bisector; from a fixed point, a circle. Turn conditions into an equation to identify it.
Worked example
The locus of points 3 units from the origin is x² + y² = 9.
Real-world uses
- Finding every position a robot arm or a car can reach within limits
- Designing safe zones
Common mistake
Describing only some of the points, leaving gaps in the locus.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Locus Problems?
Sets of points satisfying a geometric condition. It is a topic at the advanced level in Geometry.
Where is Locus Problems used in real life?
Real-world examples: Finding every position a robot arm or a car can reach within limits; Designing safe zones.
What should I learn before Locus Problems?
Make sure you are comfortable with Isoperimetric Problem, the previous topic in Geometry.
What is a common mistake with Locus Problems?
Describing only some of the points, leaving gaps in the locus.
How can I practise Locus Problems?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Locus Problems?
Move on to Geometric Proofs next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.