Question

How do you find the center of the radius of `(x-4)^2 +y^2 =16`?

Answer 1

Center: (4,0)

Radius=4

Explanation:

The circle formula is

`(x-x_1)^2+(y-y_1)^2=r^2`

The center of all circles is `(x_1,y_1)`, without the negative. The radius is the r. So we must square root the `r^2` to find r, and it will be the positive square root as length must be positive.

So from the equation

`(x-4)^2+(y^2)=16`

We can know the radius is `+sqrt16=4`

The center is `x_1, y_1`. `x_1=4` and `y_1=0`.

`y_1` is 0 as there must be a y co-ordinate of the center and the only number which allows `(y-y_1)^2=y^2` is 0