Mathematico | Mathematico

The line $y = m x$ is a tangent to the circle with equation

(x - 7)^{2} + (y - 3)^{2} = 4

Circle with two tangents

Find the two possible values of $m .$

Substitute $y = m x$ into the equation of the circle and rearrange into a quadratic equation.

The quadratic equation found in the first hint must have exactly one solution (the point of intersection between the line and the circle). What does this tell you about the discriminant?