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

Answer

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

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Precalculus

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Video Transcript

in this problem, we are given that the length of the minor axis is 16, which means that To into BS. 16 Or B equals two. The second information which is given to us about the ellipse, is that the focus? Yes, zero comma less minus six. Since the focus lies the coordinates lie on the y axis, it means the major exercise the y axis. This means the ellipse is of the form X squared by b square plus. Why square by square equals to one From here. We know that the focus is something about zero plus minus C equals, Which means that C is nothing about six. You also know that C square is nothing but a square minus me square Subsequuting this is 36 equals two. Is squared minus b squares 64. So a square is nothing, but 100 R equals to 10. Substituting the values. Here we get the question of the ellipses, X squared by these squares 64 plus. Why Square by square is 100 equals two. What? This is the equation of the alps, that's all

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