Chapter 13.6, Problem 37WE

To determine

To find: point at which the line intersects the circle.

Answer to Problem 37WE

The points are $\left(-5,0\right)\&\left(3,4\right)$ .

Explanation of Solution

Given information: The line is $x-2y=-5$ and the circle is $x^2+y^2=25$ .

Calculation:

  $\begin{array}{l}x-2y=-5\mathrm{......}\left(1\right)\\ x^2+y^2=25\mathrm{......}\left(2\right)\\ x=2y-5\mathrm{......}\left(3\right)\end{array}$

Put the value of $x$ in equation $\left(2\right)$

  $\begin{array}{l}{\left(2y-5\right)}^2+y^2=25\\ 4y^2+25-20y+y^2=25\\ 5y^2-20y=0\\ 5y\left(y-4\right)=0\\ y=0,y=4\\ x=2y-5\\ x=2\left(0\right)-5=-5\\ x=2y-5\\ x=2\left(4\right)-5=3\end{array}$

The points are $\left(-5,0\right)\&\left(3,4\right)$ .