Find the equation for the ellipse that satisf | vedclass

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(A) Length of minor axis $= 16$; foci $= (0, \pm 6)$.Since the foci are on the $y$-axis,the major axis is along the $y$-axis.Therefore,the equation of

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$\frac{x^{2}}{64} + \frac{y^{2}}{100} = 1$

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(A) Length of minor axis $= 16$; foci $= (0, \pm 6)$.Since the foci are on the $y$-axis,the major axis is along the $y$-axis.Therefore,the equation of the ellipse will be of the form $\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1$,where $a$ is the semi-major axis.Accordingly,$2b = 16 \Rightarrow b = 8$ and $c = 6$.It is known that $a^{2} = b^{2} + c^{2}$.$	herefore a^{2} = 8^{2} + 6^{2} = 64 + 36 = 100$.$\Rightarrow a = \sqrt{100} = 10$.Thus,the equation of the ellipse is $\frac{x^{2}}{8^{2}} + \frac{y^{2}}{10^{2}} = 1$ or $\frac{x^{2}}{64} + \frac{y^{2}}{100} = 1$.

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis $16$,foci $(0, \pm 6)$.

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