Find the equation for the ellipse that satisf | vedclass

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(A) Given: Foci $(\pm 3, 0)$ and $a = 4$.Since the foci are on the $x$-axis,the major axis is along the $x$-axis.Therefore,the equation of the ellipse

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$\frac{x^2}{16} + \frac{y^2}{7} = 1$

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(A) Given: Foci $(\pm 3, 0)$ and $a = 4$.Since the foci are on the $x$-axis,the major axis is along the $x$-axis.Therefore,the equation of the ellipse is of the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,where $a$ is the semi-major axis.From the foci $(\pm c, 0)$,we have $c = 3$. Given $a = 4$.We know the relation $a^2 = b^2 + c^2$.Substituting the values: $4^2 = b^2 + 3^2$.$16 = b^2 + 9$.$b^2 = 16 - 9 = 7$.Thus,the equation of the ellipse is $\frac{x^2}{16} + \frac{y^2}{7} = 1$.

Find the equation for the ellipse that satisfies the given conditions: Foci $(\pm 3, 0)$,$a = 4$.

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