Find the condition of tangency for a line $y=mx+c$ touches the ellipse

Question

$\begin{array}{1 1}(a)\;y=mx\pm \sqrt{a^2m^2+b^2}\\(b)\;y=mx\pm \sqrt{a^2m^2-b^2}\\(c)\;y=mx\pm \sqrt{am^2+b^2}\\(d)\;\text{None of these}\end{array}$