Chapter 13.1, Problem 5PSA

To determine

To verify: That the three points shown lie on the circle whose equation is $x^2+y^2=9$ .

Answer to Problem 5PSA

The points lie on the circle whose equation is $x^2+y^2=9$ .

Explanation of Solution

Given:

The figure is as follows.

  

Calculation:

To verify these points, substitute these points in the given equation and if the these points satisfy the equation then these points will lie on the circle of equation $x^2+y^2=9$ .

Take first point $\left(-3,0\right)$ .

Substitute $-3$ for $x$ and $0$ for $y$ in the equation $x^2+y^2=9$ .

  $\begin{array}{c}{\left(-3\right)}^2+{\left(0\right)}^2=9\\ 9=9\end{array}$

Take second point $\left(0,3\right)$ .

Substitute 0 for $x$ and $-3$ for $y$ in the equation $x^2+y^2=9$ .

  $\begin{array}{c}{\left(0\right)}^2+{\left(3\right)}^2=9\\ 9=9\end{array}$

Take third point $\left(3,0\right)$ .

Substitute $3$ for $x$ and $0$ for $y$ in the equation $x^2+y^2=9$ .

  $\begin{array}{c}{\left(3\right)}^2+{\left(0\right)}^2=9\\ 9=9\end{array}$

All the points satisfy the equation.

Therefore, the points lie on the circle whose equation is $x^2+y^2=9$ .