Question

Give the radius and the center for the following equation.
x^2-10x+y^2-10y=-1
center:(___,___)
radius=____

Answer 1

the equation has tobe written in standard form first
by completing the square
\[(x-5)^{2}+(y-5)^{2}=-1+5^{2}\]
\[(x-5)^{2}+(y-5)^{2}=24\]
so
\[Centre(5,5)\]
\[r ^{2}=25\]
\[r=\sqrt{24}=2\sqrt{6}\]

Answer 2

But then if it`s 2 positive 5`s then it would be positive 10, not negative 10...

Answer 3

\[x ^{2}-10x+(-5)^{2}-(-5)^{2}+y ^{2}-10y+(-y)^{2}-(-y)^{2}=-1\]
\[x ^{2}-10x+(-5)^{2}+y ^{2}-10y+(-5)^{2}=-1+(-5)^{2}+(-5)^{2}\]
\[(x-5)^{2}+(y-5)^{2}=-1+25+25=49\]
centre always changes sign so C(5,5) sorry about th radius
\[r=\sqrt{49}=7\]

Answer 4

there we go, thanks :)