Question

The equation of a circle centered at the orgin is x^2 + y^2 = 16. What is the radius of the circle

Answer 1

Given:

The equation of the circle is:

`x^2+y^2=16`

To find:

The radius of the circle.

Solution:

The standard form of a circle is:

`(x-h)^2+(y-k)^2=r^2` ...(i)

Where, (h,k) is the center and r is the radius.

We have,

`x^2+y^2=16`

In can be written as:

`x^2+y^2=4^2` ...(ii)

On comparing (i) and (ii), we get

`h=0`

`k=0`

`r=4`

Here, the center of the circle is the origin and the radius is equal to 4 units.

Therefore, the radius of the given circle is 4 units.