Question

Find the center (h,k) and the radius of a circle
5x^2-8x+ 5y^2-5y-5= 0 ??

Answer 1

start with
\[5x^2-8x+5y^2-5y=5\] then divide by 5 to get
\[x^2-\frac{8}{5}x+y^2-y=1\] the "complete the square"

Answer 2

\[(x-\frac{4}{5})^2+(y-\frac{1}{2})^2=1+\frac{16}{25}+\frac{1}{4}\]
\[(x-\frac{4}{5})^2+(y-\frac{1}{2})^2=\frac{189}{100}\]

Answer 3

center is
\[(\frac{4}{5},\frac{1}{2})\] radius is
\[\frac{\sqrt{189}}{10}\]

Answer 4

Thanks a lot!!

Answer 5

yw