For what value of $\lambda$ does the line $y=x+\lambda$ touches the ellipse $\large\frac{x^2}{36}+\frac{y^2}{25}$$=1$?

Question

$\begin{array}{1 1}(a)\;\sqrt{62}\\(b)\;\sqrt{61}\\(c)\;\sqrt{71}\\(d)\;\sqrt{82}\end{array}$