Indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola.
$\frac{x^2}{100}+y^2=1$

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

Answer: (B)

Verified step by step guidance

1. Identify the general form of the given equation: \(\frac{x^2}{100} + y^2 = 1\).
2. Recall the standard forms of conic sections: - Circle: \(\frac{x^2}{r^2} + \frac{y^2}{r^2} = 1\) (same denominators), - Ellipse: \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) (different positive denominators), - Hyperbola: \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) or \(-\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), - Parabola: equation involves only one squared term.
3. Compare the given equation to these forms: here, \(\frac{x^2}{100} + \frac{y^2}{1} = 1\) (since \(y^2\) can be seen as \(\frac{y^2}{1}\)). The denominators 100 and 1 are positive and different.
4. Since both terms are positive and the denominators are different, the equation matches the form of an ellipse.
5. Conclude that the graph of the equation \(\frac{x^2}{100} + y^2 = 1\) is an ellipse.