Solution

Show that the family of lines given by $x \cos\theta + y \sin\theta = \sqrt{a^2 \cos^2\theta + b^2 \sin^2\theta}$ where $\theta$ is a parameter and $a > b$, are all tangent to the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$.