Question

# Identify the center and ydius of each. 4x^12−16x+y^2−8y=1

Circles
Identify the center and ydius of each. $$\displaystyle{4}{x}^{{12}}−{16}{x}+{y}^{{2}}−{8}{y}={1}$$

2021-03-10

Write the equation in standard form of a circle with center (h,k) and radius r: $$\displaystyle{\left({x}−{h}\right)}^{{2}}+{\left({y}−{k}\right)}^{{2}}={r}^{{2}}$$
Isolate the variable terms and group them: $$\displaystyle{x}^{{2}}−{16}{x}+{y}^{{2}}−{8}{y}={1}$$
$$\displaystyle{\left({x}^{2}−{16}{x}\right)}+{\left({y}^{{2}}−{8}{y}\right)}={1}$$
Complete the square:
$$\displaystyle{\left({x}^{{2}}−{16}{x}+{64}\right)}+{\left({y}^{{2}}−{8}{y}+{16}\right)}={1}+{64}+{16}$$
$$\displaystyle{\left({x}−{8}\right)}^{{2}}+{\left({y}−{4}\right)}{2}={81}$$
or
$$\displaystyle{\left({x}−{8}\right)}^{{2}}+{\left({y}−{4}\right)}{2}={9}^{{2}}$$
So, the center is (8,4) and radius is 9.