How to find where a line intersects a circle

In this post I demonstrate how to find out where a line and circle intersect on a 2 dimensional plane.

Circle and line intersection

The first step is to write out the equations of a line and a circle.

We then make sure for both equations 'y' is isolated.

Once we have the equations for a line and a circle whereby 'y' is isolated, we can then go about finding the values of 'x' for where the line intersects the circle.

Like so...

Part 1

Part 2

Part 3

Part 4

After we have found the values of 'x' using the quadratic formula, we then plug them back in to y=mx+c to get the values of 'y' for which the line intersects the circle.

And that's it basically.

Below is a free interactive Desmos graph related to this work:

https://www.desmos.com/calculator/w3tsnjajtx

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