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Identify the family of curves represented by the equation x^2 + y^2 = r^2.
Identify the family of curves represented by the equation x^2 + y^2 = r^2.
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Q1
Identify the family of curves represented by the equation x^2 + y^2 = r^2.
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The equation x^2 + y^2 = r^2 represents a family of circles with varying radii 'r'.
Questions & Step-by-step Solutions
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Q
Q: Identify 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 varying radii 'r'.
Steps: 5
Show Steps
Step 1: Understand the equation x^2 + y^2 = r^2.
Step 2: Recognize that this equation is in the standard form of a circle.
Step 3: Identify that 'r' represents the radius of the circle.
Step 4: Note that as 'r' changes, the size of the circle changes.
Step 5: Conclude that the equation represents a family of circles with different radii.
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