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## A Straight Line Through a Circle

To find the coordinates where a straight line passes through a circle in four steps.

First: Get the straight line and circle equations.

Second: Replace the “y” variable in the circle equation with the straight line (remember to move $r^2$ to the other side of the equals sign).
$y=mx+c$ and $(x-a)^2+(y-b)^2=r^2$
$(x-a)^2+(mx+c-b)^2=r^2$

Third: Multiply out and factorise.
The factorised equation will give you one or two “x” values. These values are the x coordinates of where the line intercepts the circle.

Fourth: To find the corresponding y coordinate(s), plug the “x” value(s) into the original straight line equation.