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: an equation with only one squared term.
3. Compare the given equation to these forms: here, both \(x^2\) and \(y^2\) terms are positive and the sum equals 1, but the denominators under \(x^2\) and \(y^2\) are different (100 and 1 respectively).
4. Since both squared terms are positive and the denominators are different positive numbers, this matches the form of an ellipse.
5. Therefore, conclude that the graph of the equation \(\frac{x^2}{100} + y^2 = 1\) is an ellipse.