Chapter 13.6, Problem 5PSA

(a)

To determine

To find: The find whether the given point is on the graph of the circle.

Answer to Problem 5PSA

The point lies on the graph.

Explanation of Solution

Given:

The given equation is ${\left(x-3\right)}^2+{\left(y+2\right)}^2=17$ .

The given point is $\left(4,2\right)$ .

Calculation:

Consider the given equation is,

  ${\left(x-3\right)}^2+{\left(y+2\right)}^2=17$

Substitute the given point in the above equation as,

  $\begin{array}{l}{\left(4-3\right)}^2+{\left(2+2\right)}^2=17\\ 1+16=17\\ 17=17\end{array}$

As, the LHS is equal to RHS the point lies on the graph.

(b)

To determine

To find: The find whether the given point is on the graph of the circle.

Answer to Problem 5PSA

The point do not lies on the graph.

Explanation of Solution

Given:

The given equation is ${\left(x-3\right)}^2+{\left(y+2\right)}^2=17$ .

The given point is $\left(3,-2\right)$ .

Calculation:

Consider the given equation is,

  ${\left(x-3\right)}^2+{\left(y+2\right)}^2=17$

Substitute the given point in the above equation as,

  $\begin{array}{l}{\left(3-3\right)}^2+{\left(-2+2\right)}^2=17\\ 0+0=17\\ 0\ne 17\end{array}$

As, the LHS is not equal to RHS the point do not lies on the graph.