Family of Curves/Examples/Circles with Centers along x-Axis

Example of Family of Curves

Consider the equation:

$(1): \quad \paren {x - h}^2 + y^2 = a^2$

where $x, y, a, h \in \R$.

$(1)$ defines a family of circles:

whose radii are determined by the parameter $a$

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.