Find the Points of Intersection of A Circle and a Line

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A step by step worksheet to find the points of intersection of a circle and a line is presented. Unlimited number of practice questions may be generated along with their solutions. The graph of the line and the circle are shown at the bottom of the page with the points of intersection if any.

Step by step solution

STEP 1: Solve for $y$ the equation of the line.

STEP 2: Substitute $y$ by the above expression into the equation of the circle to obtain an equation in $x$ only.

STEP 3: Expand the above equation and simplify and write in standard form.

STEP 4: Solve the above equation for $x$ and use the equation of the line to find $y$. If the equation obtained in step 3 does not have a solution, it means the circle and the line do not intersect.

Graphical Meaning of Solution

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

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