Chapter 9.5, Problem 5PSA

To determine

Tocalculate: The area of a circle that passes through point at $\left(9,-4\right)$ and center $\left(-3,5\right)$ .

Answer to Problem 5PSA

The area of a circle that passes through point at $\left(9,-4\right)$ and center $\left(-3,5\right)$ is $225\pi$ .

Explanation of Solution

Given information:

Circle passes through $\left(9,-4\right)$ and center $\left(-3,5\right)$ .

Formula used:

The distance between two points by using the distance formula, which is an application of the Pythagoreantheorem.

D $=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Area of Circle, A=πr²

Calculation:

  

  $\begin{array}{l}r=\sqrt{{\left(9-(-3)\right)}^2+{\left(-4-5\right)}^2}\\ =\sqrt{144+81}\\ =\sqrt{225}\\ =15\\ A=\pi r^2\\ $ =\pi {(15)}^2$=225\pi \end{array}$