Question

How do you find the center and radius for `x^2 + (y + 6)^2 = 49`?

Answer 1

centre = (0 ,-6) , radius = 7

Explanation:

The standard form of the equation of a circle is.

`color(red)(bar(ul(|color(white)(a/a)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(a/a)|)))`
where (a ,b) are the coordinates of the centre and r, the radius.

`x^2+(y+6)^2=49" is in this form."`

That is `(x-0)^2+(y-(-6))^2=7^2`

and by comparison with the standard form.

`a=0,b=-6" and " r=7`

Thus, centre = (0 ,-6) and radius = 7