# Question #b8410

##### 1 Answer
May 21, 2015

Since there are an infinite number of points along the line $y = 2 x - 1$ which could be the center of the proposed circle, there is no single equation for a circle with a center on this line.

For any arbitrary constant $\hat{x}$
the equation would be
${\left(x - \hat{x}\right)}^{2} + {\left(y - 2 \hat{x} + 1\right)}^{2} = {3}^{2}$

As examples:
$\hat{x} = 0 \rightarrow {x}^{2} + {\left(y + 1\right)}^{2} = 9$
$\hat{x} = 1 \rightarrow {\left(x - 1\right)}^{2} + {\left(y - 1\right)}^{2} = 9$