Question

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

Answer 1

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

Explanation:

`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`