One-Parameter Family of Curves/Examples/Circles of Equal Radius with Centers along x-Axis
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Example of One-Parameter Family of Curves
Consider the equation:
- $(1): \quad \paren {x - h}^2 + y^2 = a^2$
where $a$ is constant.
$(1)$ defines a one-parameter family of circles of constant radius $a$ whose centers are on the $x$-axis of a Cartesian plane at $\tuple {h, 0}$ determined by values of the parameter $h$.
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.