# Intersections of Circles and Straight Lines

This applet investigates how to solve equations by seeing where a straight line intersects a circle.

###### Author and programmer: Ron Barrow

UK Years 10-12, KS4, KS5, Higher GCSE Mathematics, Grades C - A*, Core AS Level - Number, Algebra and Graphs

TweetInstructions below See also: Solving Equations Graphically Equations of Circles

## How to Use this Applet

Look at the initial position of the circle and the straight line on the graph. You can see that they cross in two places. What are the coordinates of the points where they cross, and how does that tie in with the solution of the two simultaneous equations at the right of the screen?

Look at that equations carefully.

They can be solved by substituting for `x` or `y` and then solving a quadratic equation.

You can vary the straight line graph by clicking A+, A-, B+, B-, C+ and C-. You can vary the radius of the circle by clicking Radius+ or Radius-.

Go ahead. Try it. Are there always solutions? How many? Sometimes only one? Investigate!