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The given equation is:

\[
C_1 = \{(x,y) \in \mathbb{R}^2 : x^2 + y^2 - 4x + 9y - 3 = 0\}
\]

We need to find the center and the radius of the circle by transforming this into the standard form of a circle's equation, which is:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Here, \((h,k)\) is the center, and \(r\) is the radius of the circle.

### Step 1: Complete the square for \(x\) and \(y\).

The equation is:

\[
x^2 + y^2 - 4x + 9y - 3 = 0
\]

#### Completing the square for \(x\):
\[
x^2 - 4x \quad \text{(take half of \(-4\), square it:} \left(\frac{-4}{2}\right)^2 = 4)
\]
\

Averigüen el centro y el radio de la siguiente circunferencia: x^2 + y^2 - 4x + 9y - 3 = 0

Learn how to find the center and radius of the circle given by the equation x^2 + y^2 - 4x + 9y - 3 = 0. This problem involves completing the square and rewriting the equation in its standard form. Suitable for students in Grades 10-12.

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