## Lines intersecting circles

When a line intersects a circle it will either have one point of contact in which case it is a tangent to the circle or it will cut it in two places.

To find the points of contact between a line and a circle

- If needed, rearange the equation of the line to make x or y the subject
- Substitute into the circle equation and solve the resulting quadratic
- Substitute the solutions into the equation of the line to get the required coordinates

Example

Find where the line intersects with the circle

When we substitute y into the circle we get

or

If

If

the points of intersection are and

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Categories: Graphing

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