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What is the general form of the family of curves represented by the equation x^2
What is the general form of the family of curves represented by the equation x^2 + y^2 = r^2?
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Practice Questions
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Q1
What is the general form of the family of curves represented by the equation x^2 + y^2 = r^2?
Circles with radius r
Ellipses with semi-major axis r
Hyperbolas with transverse axis r
Straight lines with slope r
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The equation x^2 + y^2 = r^2 represents a family of circles with radius r centered at the origin.
Questions & Step-by-step Solutions
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Q
Q: What is the general form of the family of curves represented by the equation x^2 + y^2 = r^2?
Solution:
The equation x^2 + y^2 = r^2 represents a family of circles with radius r centered at the origin.
Steps: 6
Show Steps
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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