# If $y=mx+c$ is a tangent to the ellipse $x^2+2y^2=6$ then $c^2$ is equal to

$\begin{array}{1 1}(A)\;36/m^2 \\(B)\;6m^2-3 \\(C)\;3m^2-3 \\(D)\;6m^2+3 \end{array}$

If $y=mx+c$ is a tangent to
$\large\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
then $c^2=a^2m^2+b^2$
Here $a^2=6$
$b^2=3$
$c^2=6m^2+3$
Hence D is the correct answer.