Question

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

Circles
ANSWERED
asked 2021-03-09
Identify the center and ydius of each. \(\displaystyle{4}{x}^{{12}}−{16}{x}+{y}^{{2}}−{8}{y}={1}\)

Answers (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.

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