What is the general form of the equation of a circle with a center at (7, 0) and a radius of 10?

Nov 12, 2015

${x}^{2} - 14 x + {y}^{2} - 51 = 0$

Explanation:

First, let's write the equation in standard form.

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

$\implies {\left(x - 7\right)}^{2} + {\left(y - 0\right)}^{2} = {10}^{2}$

$\implies {\left(x - 7\right)}^{2} + {y}^{2} = {10}^{2}$

Then, we expand the equation.

$\implies \left({x}^{2} - 14 x + 49\right) + {y}^{2} = 100$

Finally, let's put all the terms in one side and simplify

$\implies {x}^{2} - 14 x + 49 + {y}^{2} - 100 = 0$

$\implies {x}^{2} - 14 x + {y}^{2} - 51 = 0$