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# The straight line $2x-y+c=0$ is a tangent to the ellipse $4x^{2}+8y^{2}=32$ if $c$ is

$\begin{array}{1 1}(1)\pm 2\sqrt{3}&(2)\pm 6\\(3)36&(4)\pm4\end{array}$

Can you answer this question?

The equation of the ellipse is
$4x^2+8y^2=32$
$\large\frac{4x^2}{32} + \frac{8y^2}{32} $$=1 \large\frac{x^2}{8} + \frac{y^2}{4}$$=1$-----(1)
The equation of the line is
$2x-y+c=0$
$y=2x+c$ ------(2)