The eccentricity of the conic 16x^2 + 7y^2 = | vedclass

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(C) Given the equation of the conic: $16x^2 + 7y^2 = 112$.Dividing both sides by $112$,we get:$\frac{16x^2}{112} + \frac{7y^2}{112} = 1$$\frac{x^2}{7}

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$3/4$

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(C) Given the equation of the conic: $16x^2 + 7y^2 = 112$.Dividing both sides by $112$,we get:$\frac{16x^2}{112} + \frac{7y^2}{112} = 1$$\frac{x^2}{7} + \frac{y^2}{16} = 1$.This is an equation of an ellipse of the form $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$,where $a^2 = 16$ and $b^2 = 7$.Since $a^2 > b^2$,the eccentricity $e$ is given by the formula $e = \sqrt{1 - \frac{b^2}{a^2}}$.Substituting the values: $e = \sqrt{1 - \frac{7}{16}} = \sqrt{\frac{16 - 7}{16}} = \sqrt{\frac{9}{16}} = \frac{3}{4}$.

The eccentricity of the conic $16x^2 + 7y^2 = 112$ is

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