Chapter 1.8, Problem 88E

To determine

To calculate: Thecenter and radius of the circle $x^2+y^2=5$ and sketch the graph of the circle.

Answer to Problem 88E

The center of the circle is $\left(0,0\right)$ and radius is $\sqrt{5}$ units. The graph of the circle is provided below,

  

Explanation of Solution

Given information:

The equation $x^2+y^2=5$ .

Formula used:

The standard form of the equation of the circle is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ , where $\left(h,k\right)$ denote the center of the circle and r denote the radius.

Calculation:

Consider the equation $x^2+y^2=5$ .

Rewrite the equation as,

  ${\left(x-0\right)}^2+{\left(y-0\right)}^2={\left(\sqrt{5}\right)}^2$

Recall that the standard form of the equation of the circle is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ , where $\left(h,k\right)$ denote the center of the circle and r denote the radius.

Compare, ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ and ${\left(x-0\right)}^2+{\left(y-0\right)}^2={\left(\sqrt{5}\right)}^2$ .

Here, $h=0,k=0\text{ and }r=\sqrt{5}$ .

Therefore, center of circle is $\left(0,0\right)$ and radius is $\sqrt{5}$ .

Now, on the Cartesian plane construct a circle with center at origin and radius $\sqrt{5}$ units.

The graph obtained is provided below,

  

Thus, the center of the circle is $\left(0,0\right)$ and radius is $\sqrt{5}$ units.