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andii1101
04.04.2020 •
Mathematics
Write an equation for an ellipse centered at the origin, which has foci at (\pm8,0)(±8,0)left parenthesis, plus minus, 8, comma, 0, right parenthesis and vertices at (\pm17,0)(±17,0)left parenthesis, plus minus, 17, comma, 0, right parenthesis
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Ответ:
The equation of the ellipse is![\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1](/tpl/images/0581/0202/52547.png)
Step-by-step explanation:
The standard form of the equation of an ellipse with center (0 , 0) is
, where
The coordinates of the vertices are (± a , 0) The coordinates of the foci are (± c , 0) , where c ² = a² - b²∵ The ellipse is centered at the origin
∴ The center of it is (0 , 0)
∵ It has foci at (± 8 , 0)
- The coordinates of the foci are (± c , 0)
∴ c = ±8
∵ It has Vertices at (± 17 , 0)
- The coordinates of the vertices are (± a , 0)
∴ a = ±17
∵ c² = a² - b²
- Substitute the values of c and a to find b
∴ (8)² = (17)² - b²
∴ 64 = 289 - b²
- Add b² to both sides
∴ b² + 64 = 289
- Subtract 64 from both sides
∴ b² = 225
- Take √ for both sides
∴ b = ± 15
∵ The equation of the ellipse is![\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1](/tpl/images/0581/0202/5a79a.png)
- Substitute the values of a and b in it
∴
⇒
∴ The equation of the ellipse is
Ответ:
each pound is equal to three dollars.