Question

How do you find the center and radius for `x^2 + y^2 +2x -2y -14 = 0`?

Answer 1

The circle has the center in `(-1;1)` and the radius of `4`

Explanation:

To find the center and radius we have to transform the equation to form:

`(x-a)^2+(y-b)^2=r^2`

We start from:

`x^2+2x+y^2-2y-14=0`

We transform it to:

`x^2+2x color(red)(+1)+y^2-2ycolor(red)(+1)-14 color(red)(-2)=0`

I added `1` to transform the formulas to `(a+-b)^2`. If I added `2` then I had to substract `2` to keep the equation balanced. These operation are marked in red.

`(x+1)^2+(y-1)^2-16=0`

`(x+1)^2+(y-1)^2=16`

From this equation we read that: the centre is `(-1;1)` and the radius is `r=4`