Mathematics

A line is tangent to a parabola when it touches the curve at exactly one point—meaning the system of equations has exactly one solution. Set the line equal to the parabola and rearrange into a quadratic; tangency occurs when the discriminant equals zero. Solving for $m$ using this condition will give you the slopes of both possible tangent lines.

A line is tangent to a parabola when it touches the curve at exactly one point—meaning the system of equations has exactly one solution. Set the line equal to the parabola and rearrange into a quadratic; tangency occurs when the discriminant equals zero. Solving for $m$ using this condition will give you the slopes of both possible tangent lines.