# How do you find the equation of the circle given Radius 3 and Tangent to y-axis at (0,4)?

The phrase, "Tangent to the y-axis at $\left(0 , 4\right)$", tells us that the y coordinate of the center is 4. The phrase "given radius 3" tells us that the x coordinate of the center can be either -3 or 3 but there is no way to know which. Therefore, the equation of the circle is either:
${\left(x - - 3\right)}^{2} + {\left(y - 4\right)}^{2} = {3}^{2}$ or ${\left(x - 3\right)}^{2} + {\left(y - 4\right)}^{2} = {3}^{2}$