Pregunta
\[ \begin{array}{l}(x+2)^{2}+(y+6)^{2}=9 \\ \text { Part } 1 \text { of } 2 \\ \text { The center is }(\square, \square) \\ \text { Part } 2 \text { of } 2\end{array} \] The radius is \( r=\square \)
Ask by Mccoy Todd. in the United States
Feb 25,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The center is (–2, –6) and the radius is 3.
Solución
The given circle equation is (x + 2)² + (y + 6)² = 9.
Part 1 of 2:
The center of the circle is (–2, –6).
Part 2 of 2:
Since the equation equals 9, and the standard form of a circle is (x – h)² + (y – k)² = r², the radius is r = √9 = 3.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
The given equation \((x+2)^{2}+(y+6)^{2}=9\) describes a circle in standard form, where the center can be derived from the expression inside the parentheses. Thus, the center of the circle is at \((-2, -6)\). As for the radius, the equation equals \(r^2\). Since 9 is the square of the radius, we find that the radius \(r\) is equal to 3 (because \(\sqrt{9} = 3\)). So, to summarize, the center is \((-2, -6)\) and the radius is \(3\).
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