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.