Family of Curves/Examples/Circles in Plane

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.