Equation from centre and radius

Problem

Write the equation of the circle with centre $C(2;-1)$ and radius $3$.

Solution

We start from the “vertex” form with $x_0 = 2$, $y_0 = -1$, $R = 3$: $(x - 2)^2 + (y + 1)^2 = 9.$ Expanding the squares gives the standard form: $x^2 - 4x + 4 + y^2 + 2y + 1 = 9 \implies \boxed{x^2 + y^2 - 4x + 2y - 4 = 0.}$

Links

Topics: Circonferenza analitica
Concepts: Centro · Equazione circonferenza · Forma standard · Forma vertice · Raggio
Methods: Circonferenza equazione
Skills: Geometria analitica · Usare formule
Exercise types: Problema geometrico