Question

Help please! Solve each system. In your work, identify the shape of the graph of each equation. x^2+y^2+2x+2y=0
x^2+y^2+4x+6y+12=0

Answer 1

\(\normalsize\color{blue}{ x^2+y^2+2x+2y=0 }\)
\(\normalsize\color{blue}{ x^2+2x+y^2+2y=0 }\)
\(\normalsize\color{blue}{ x^2+2x\color{red}{+1 } +y^2+2y\color{green}{+1 } =0 \color{red}{+1 } \color{green}{+1 } }\)
\(\normalsize\color{blue}{ x^2+2x+1+~y^2+2y+1=2 }\)
\(\normalsize\color{blue}{ \underline{x^2+2x+1}+ \underline{y^2+2y+1}=2 }\)
\(\normalsize\color{blue}{ (x+1)^2+(y+1)^2=2 }\)
\(\normalsize\color{blue}{ (x+1)^2+(y+1)^2=\sqrt{2}^{2} }\)

Answer 2

Compare this one to the equation of the circle, \(\normalsize\color{blue}{ (x-h)^2+(y-k)^2=r ^{2} }\) where `(h,k)` is the center.

Answer 3

The other one,
\(\normalsize\color{blue}{ x^2+y^2+4x+6y+12=0 }\)
\(\normalsize\color{blue}{ x^2+4x+12+y^2+6y=0 }\)
\(\normalsize\color{blue}{ x^2+4x+4+8+y^2+6y=0 }\)
\(\normalsize\color{blue}{ x^2+4x+4+y^2+6y+8=0 }\)
\(\normalsize\color{blue}{ x^2+4x+4+y^2+6y+8\color{red}{+1}=0\color{red}{+1} }\)
\(\normalsize\color{blue}{ \underline{ x^2+4x+4 } +\underline{ y^2+6y+9}=1 }\)
\(\normalsize\color{blue}{ (x+2)^2 +(y+3)^2=1 }\)
\(\normalsize\color{blue}{ (x+2)^2 +(y+3)^2=1^2 }\)

Answer 4

Compare this one also to \(\normalsize\color{blue}{ (x-h)^2 +(y-k)^2=r^2 }\) .


Good LUCK !

Answer 5

thank you so much

Answer 6

Do you see the centers and the radiuses ?

Answer 7

um sure can you still post them my parents are making me leave the house for a few minutes sadly but i would appreciate it

Answer 8

Yes :) radius center
Circle 1 ─ √2 (-1,-1)
Circle 2 ─ 1 (-2,-3)

Answer 9

Good luck !

Answer 10

ntw I am also about to leave:) Basketball

Answer 11

btw (not ntw)

Answer 12

ok good luck and thanks :D