What is the general form of the family of curves represented by the equation x^2 + y^2 = r^2?
Correct Answer: Circles with radius r centered at the origin.
- Step 1: Understand the equation x^2 + y^2 = r^2. This is a mathematical equation.
- Step 2: Recognize that 'x' and 'y' are variables that represent points on a graph.
- Step 3: Identify 'r' as a constant that represents the radius of a circle.
- Step 4: Note that the equation describes all points (x, y) that are a distance 'r' from the center.
- Step 5: Understand that the center of the circle is at the point (0, 0) on the graph.
- Step 6: Conclude that the equation represents a circle with radius 'r' centered at the origin.
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