CBSE · Class 10 · Mathematics · Coordinate GeometryQuestion 1: Equation of a Circle
Step-by-Step Solution
Theorem and Equation of a Circle
Theorem
\nThe equation of a circle with center (a, b) and radius r is given by (x - a)^2 + (y - b)^2 = r^2.
Proof
\nLet P(x, y) be any point on the circle with center (a, b) and radius r. Then, by definition of a circle, the distance of P from the center is equal to the radius. \nUsing the distance formula, we have:
\sqrt{(x - a)^2 + (y - b)^2} = r \nSquaring both sides, we get:
(x - a)^2 + (y - b)^2 = r^2 \nThis is the required equation of the circle.
Example
\nFind the equation of the circle with center (2, 3) and radius 4.
💡 Study Guide: This question tests core syllabus concepts from Coordinate Geometry. For formulas, key summaries, and mock exam reference guides, read the full Coordinate Geometry Revision Notes.