Find the Points of Intersection of Two Circles

A step by step interactive worksheet to solve problems related to the intersection of two circles is presented. Practice questions are also generated with their solutions. The graph two circle are plotted at the bottom of the page and show the points of intersection if any.

Step by step solution


STEP 1: If $(x,y)$ is be the point of intersection of the two circles, then $(x,y)$ is a solution to the simultaneous system of equations shown below.




STEP 2: Expand and simplify the squares in the equations in step 1.




STEP 3: Subtract the lower equation from the upper equation and simplify.




STEP 4: Substitute $y$ in one of the equations of step 1 by the last expression found in step 3.




STEP 5: Write the above quadratic equation in standard form and solve it, then use the linear equation found in step 3 to find $y$.




Graphical Meaning of Solution



Below are shown the graphs of the two circles and the point of intersection if there are any. (Change scales if necessary)


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