I need help with this maths question...

Prove that if the line $\displaystyle lx +my + n = 0$ touches the ellipse $\displaystyle b^2 x^2 + a^2 y^2 = a^2 b^2$ then $\displaystyle a^2 l^2 + b^2 m^2 = n^2$

I tried substituting the first equation in terms of x or y, then substitute into the second equation but I ended up having too many unknowns.... any ideas how to solve this question...

Thank you..