How do you write the equation of the circle in standard form $x^2 + y^2 + 2x + 4y - 4091 = 0$ ?

Question

2647 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-13T12:55:19

Completing the square in $x$ and $y$ . See below

$x^2+y^2+2x+4y-4091=(x+1)^2+(y+2)^2-1-4-4091=(x+1)^2+(y+2)^2-4096=(x+1)^2+(y+2)^2-64^2$

Finally we have

$(x+1)^2+(y+2)^2=64^2$ this is the equation of a circle with center in $(-1,-2)$ and radius $r=64$

How do you write the equation of the circle in standard form x^2 + y^2 + 2x + 4y - 4091 = 0x^2 + y^2 + 2x + 4y - 4091 = 0?