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(C) The equation of the ellipse is $\frac{x^2}{9} + \frac{y^2}{4} = 1$.Comparing this with the standard form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,w

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$\pm \sqrt{9m^2 + 4}$

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(C) The equation of the ellipse is $\frac{x^2}{9} + \frac{y^2}{4} = 1$.Comparing this with the standard form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,we get $a^2 = 9$ and $b^2 = 4$.The condition for the line $y = mx + c$ to be a tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is $c^2 = a^2m^2 + b^2$.Substituting the values of $a^2$ and $b^2$,we get $c^2 = 9m^2 + 4$.Therefore,$c = \pm \sqrt{9m^2 + 4}$.

If $y = mx + c$ is a tangent to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,then the value of $c$ is

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