Chapter 11.3, Problem 4QR

To determine

To find: Therectangular equation of a circle of radius 8 centered at the origin.

Answer to Problem 4QR

The rectangular form of the circle is $x^2+y^2=25$ .

Explanation of Solution

Given information:

Radius = 5

Center of the circle is at origin.

Formula used:

Rectangular form of a circle with center $\left(a,b\right)$ and radius $r$ :

  ${\left(x-a\right)}^2+{\left(y-b\right)}^2=r^2$

Calculation:

Given that the center of the circle is at origin.

Thus, the coordinates of the center is $\left(0,0\right)$ .

Now, find the rectangular form of the circle.

Substitute the value of radius and the coordinate of the center. Use the expression ${\left(x-a\right)}^2+{\left(y-b\right)}^2=r^2$

  $\begin{array}{c}{\left(x-0\right)}^2+{\left(y-0\right)}^2=5^2\\ x^2+y^2=25\end{array}$

Conclusion:

Hence, the required rectangular form of the circle is $x^2+y^2=25$ .