📍 Locus of a Point – Concept and All Common Types

In geometry, the locus of a point is the set of all positions (points) that satisfy a particular condition or set of conditions. Let’s explore the different types of loci with clear examples and visuals.

1️⃣ Locus of a Point Equidistant from a Fixed Point – Circle

This is the most basic and common locus:

• The set of points that are always at a constant distance from a fixed point (called the center).
• The fixed distance is called the radius.

2️⃣ Locus of a Point Equidistant from Two Fixed Points – Perpendicular Bisector

If a point moves such that it is always equidistant from two fixed points \( A \) and \( B \), its path forms the perpendicular bisector of segment \( AB \).

3️⃣ Locus of a Point Equidistant from a Given Line – Parallel Line

The locus of a point that remains at a constant perpendicular distance from a given line is a line parallel to the given line.

4️⃣ Locus of a Point Equidistant from Two Intersecting Lines – Angle Bisector

If two lines intersect and a point moves such that it maintains equal distance from both lines, the locus of that point is the angle bisector of the angle formed between them.

📌 Summary Table of Common Loci

🎯 Final Thought

Understanding loci helps in solving coordinate geometry, construction, and distance-related problems in competitive exams. Always ask: “What is fixed?” and “What must remain equal or constant?” That leads directly to the correct path—literally!

Explore the path of logic through geometry! 🧭