Question

write the equation in standard form for the circle $x^{2}+y^{2}-18x = 19$.

Explanation:

Step1: Group x-terms together

$x^2 - 18x + y^2 = 19$

Step2: Complete the square for x

Take half of -18: $\frac{-18}{2}=-9$, square it: $(-9)^2=81$. Add 81 to both sides.
$x^2 - 18x + 81 + y^2 = 19 + 81$

Step3: Rewrite as perfect squares

$(x-9)^2 + y^2 = 100$

Answer:

$(x-9)^2 + y^2 = 100$