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Sophie [7]
3 years ago
11

Write an equation for an ellipse centered at the origin, which has foci at (0,\pm\sqrt{63})(0,± 63 ​ )left parenthesis, 0, comma

, plus minus, square root of, 63, end square root, right parenthesis and vertices at (0,\pm\sqrt{91})(0,± 91 ​ )left parenthesis, 0, comma, plus minus, square root of, 91, end square root, right parenthesis.
Mathematics
1 answer:
steposvetlana [31]3 years ago
8 0

Answer:

\frac{x^{2} }{4312 } + \frac{y^{2} }{8281 }

Step-by-step explanation:

Since the foci are at(0,±c) = (0,±63) and vertices (0,±a) = (0,±91), the major axis is the y- axis. So, we have the equation in the form (with center at the origin) \frac{x^{2} }{b^{2} } + \frac{y^{2} }{a^{2} }.

We find the co-vertices b from b = ±√(a² - c²) where a = 91 and c = 63

b = ±√(a² - c²)

= ±√(91² - 63²)

= ±√(8281 - 3969)

= ±√4312

= ±14√22

So the equation is

\frac{x^{2} }{(14\sqrt{22}) ^{2} } + \frac{y^{2} }{91^{2} } = \frac{x^{2} }{4312 } + \frac{y^{2} }{8281 }

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