If the line y = 4x + c is a tangent to the el | vedclass

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(D) The equation of the ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,where $a^2 = 8$ and $b^2 = 4$.The condition for the line $y = mx + c$ to be

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$\pm \sqrt{132}$

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(D) The equation of the ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,where $a^2 = 8$ 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 $c^2 = a^2m^2 + b^2$.Given $m = 4$,$a^2 = 8$,and $b^2 = 4$.Substituting these values into the condition:$c^2 = 8(4)^2 + 4$$c^2 = 8(16) + 4$$c^2 = 128 + 4$$c^2 = 132$$c = \pm \sqrt{132}$.

If the line $y = 4x + c$ is a tangent to the ellipse $\frac{x^2}{8} + \frac{y^2}{4} = 1$,then $c = \dots$

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