Indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola.
$5x^2+5y^2=180$

• A. A circle
• B. An ellipse
• C. A hyperbola
• D. A parabola

Answer: (A)

Verified step by step guidance

1. Start with the given equation: \$5x^2 + 5y^2 = 180$.
2. Divide every term in the equation by 5 to simplify it: \(\frac{5x^2}{5} + \frac{5y^2}{5} = \frac{180}{5}\), which simplifies to \(x^2 + y^2 = 36\).
3. Recognize the standard form of the equation: \(x^2 + y^2 = r^2\), where \(r^2\) is a positive constant.
4. Recall that the equation \(x^2 + y^2 = r^2\) represents a circle centered at the origin with radius \(r\).
5. Since both \(x^2\) and \(y^2\) have the same positive coefficient after simplification, the graph is a circle.