How do you write the equation for a circle with a center (-5,4); tangent (touching at one point) to the x-axis?

Jun 6, 2016

${x}^{2} + {y}^{2} + 10 x - 8 y + 25 = 0$

Explanation:

$r = 4$ because the circle is tangent to the x-axis
therefore the equation is:

${\left(x + 5\right)}^{2} + {\left(y - 4\right)}^{2} = 16$

${x}^{2} + 10 x + 25 + {y}^{2} - 8 y + 16 - 16 = 0$

${x}^{2} + {y}^{2} + 10 x - 8 y + 25 = 0$