Family of Curves/Examples/Circles in Plane
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Example of Family of Curves
Consider the equation:
- $(1): \quad \paren {x - h}^2 + \paren {y - k}^2 = a^2$
$(1)$ defines a family of circles:
- whose radii are determined by the parameter $a$
- whose centers are at $\tuple {h, k}$ on Cartesian plane, determined by values of the parameters $h$ and $k$.
Hence $(1)$ represents the family of all circles in the plane.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): family: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): family: 1.