Chapter 8.3, Problem 25E

Solution

Write the standard form of the equation of the circle with the given radius and with the center at origin.

  $x^2+y^2=256$

Given information:

Given radius is:

  $16$ .

Formula used:

Standard form of equation of a circle with radius ‘ r’ and center $\left(h,k\right)$ is

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

Calculation:

In order to write the standard form of the equation of the circle with the given radius and it’s center is the origin, use the standard form of the equation of the circle:

  ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ , with radius ‘ r’ and center $\left(h,k\right)$ .

Note that the centre of given circle is origin and the radius of the circle is $16$ , i.e. here

  $\left(h,k\right)=\left(0,0\right),r=16$

Thus, the equation becomes:

  $\begin{array}{c}{\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2\\ {\left(x-0\right)}^2+{\left(y-0\right)}^2={16}^2\\ x^2+y^2=256\end{array}$

Thus, the standard form of the equation of circle with given information is:

  $x^2+y^2=256$