Any line that intersects an ellipse in just 1 point is necessarily a tangent line.

Question

I know that that the equation of an ellipse tangent line passing through a given point $M(x_0,y_0) \in (ellipse) $ is $$\frac{xx_0}{a^2} + \frac{yy_0}{b^2} = 1$$ but I can't prove that if a line intersects ellipse in just 1 point then it's necessarily a tangent line.

Thank you.