Question

Think about all of the ways in which a line and a circle can intersect.

Select all of the number of ways in which a line and a circle can intersect.

0

1

2

3

4

infinitely many

Answer 1

0, 1, 2.

Reason: geometrically a line can miss the circle (0), be tangent to it (1), or cut it at two points (2). Algebraically, substituting a line into a circle's equation gives a quadratic in one variable, which has at most two real solutions. It cannot meet a (nondegenerate) circle in 3, 4, or infinitely many points.