Chapter 9.2, Problem 2OE

To determine

To calculate: The center and radius of the circle.

Answer to Problem 2OE

The center and radius of the circle are $\left(0,0\right)$ and $1$ respectively.

Explanation of Solution

Given information: The equation of the circle is $x^2+y^2=1$ .

Formula used: $x^2+y^2+2gx+2fy+c=0$ and $r=\sqrt{g^2+f^2-c}$

Calculation: As we know that $\left(-g,-f\right)$ is the center of a circle and $r=\sqrt{g^2+f^2-c}$ is the radius of a circle.

Thus, comparing $x^2+y^2-1=0$ to $x^2+y^2+2gx+2fy+c=0$ , we get,

  $\begin{array}{ccc}2g=0& 2f=0& \\ g=0& f=0& c=-1\end{array}$

Therefore, the center of the given circle $\left(-g,-f\right)=\left(0,0\right)$

Now, find the radius,

  $\begin{array}{l}r=\sqrt{g^2+f^2-c}\\ r=\sqrt{0+0-\left(-1\right)}\\ r=\sqrt{1}\\ \therefore r=1\end{array}$

Hence, the required center and radius of the circle are $\left(0,0\right)$ and $1$ respectively.