Intersection of a Line and a Circle (Leaving Cert Mathematics): Flashcards

A line that intersects a circle at exactly one point

The single point where a tangent meets a circle

No intersection, two points, one point (tangent)

Simultaneous equations

Express line as $y=...$ or $x=...$ form

Substitute into the circle equation

Line intersects circle at two points

Line is tangent to the circle

Line doesn't intersect the circle

To avoid fractions where possible

Substitute points back into both original equations