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

No intersection, 1 point (tangent), 2 points

Line does not touch circle ($\Delta < 0$)

Line is tangent to circle ($\Delta = 0$)

Line crosses through circle ($\Delta > 0$)

$(x - h)^2 + (y - k)^2 = r^2$

$y = mx + c$

Substitute line equation into circle equation

A quadratic equation in $x$

$\Delta = b^2 - 4ac$

Two points of intersection

One point of intersection (tangent)

No intersection