For the ellipse 25x^2 + 9y^2 - 150x - 90y + 2 | vedclass

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(C) The given equation of the ellipse is $25x^2 + 9y^2 - 150x - 90y + 225 = 0$. Rearranging the terms,we get $25(x^2 - 6x) + 9(y^2 - 10y) = -225$. Com

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(C) The given equation of the ellipse is $25x^2 + 9y^2 - 150x - 90y + 225 = 0$. Rearranging the terms,we get $25(x^2 - 6x) + 9(y^2 - 10y) = -225$. Completing the square,$25(x - 3)^2 - 225 + 9(y - 5)^2 - 225 = -225$. This simplifies to $25(x - 3)^2 + 9(y - 5)^2 = 225$. Dividing by $225$,we get $\frac{(x - 3)^2}{9} + \frac{(y - 5)^2}{25} = 1$. Here,$a^2 = 9$ and $b^2 = 25$. Since $b^2 > a^2$,the ellipse is vertical. The eccentricity $e$ is given by $e = \sqrt{1 - \frac{a^2}{b^2}} = \sqrt{1 - \frac{9}{25}} = \sqrt{\frac{16}{25}} = \frac{4}{5}$.

For the ellipse $25x^2 + 9y^2 - 150x - 90y + 225 = 0$,the eccentricity $e$ is: (in $/5$)

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