Matching graphs to their standard form equations is a fundamental skill in geometry, particularly when dealing with conic sections (circles, ellipses, parabolas, and hyperbolas). Each conic section has a specific standard form equation that reveals key features like the center, radius, vertices, and axes. By recognizing these features from the graph, you can accurately match the graph to its corresponding equation. This activity reinforces your understanding of how algebraic representations connect to geometric shapes, and it enhances your problem-solving skills.
Match the term with its correct definition.
| Term | Definition |
|---|---|
| 1. Circle | A. The set of all points in a plane that are equidistant from a fixed point (center). |
| 2. Ellipse | B. The set of all points in a plane such that the sum of the distances from two fixed points (foci) is constant. |
| 3. Parabola | C. The set of all points in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus). |
| 4. Hyperbola | D. The set of all points in a plane such that the absolute difference of the distances from two fixed points (foci) is constant. |
| 5. Standard Form | E. A way of writing equations that makes it easy to identify key features of the graph. |
Match the numbers to the letters. (Example: 1 - A)
Complete the following paragraph with the correct terms. Each term is used only once: center, radius, focus, vertex, conic sections.
The graphs of circles, ellipses, parabolas, and hyperbolas are called _______. A circle's equation reveals its _______ and _______. A parabola has a _______, and the turning point is called the _______.
Explain how changing the values in the standard form equation of a circle, $(x-h)^2 + (y-k)^2 = r^2$, affects the position and size of the circle on the coordinate plane.
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