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What is the standard equation for the ellipse with the given characteristics?
1. foci: (-10, 0) and (10, 0); co-vertices: (0, -3), (0, 3)
2. co-vertices: (-20, 0) and (20, 0); foci: (0, -8) and (0, 8)
1 Answer
- HemantLv 71 decade agoFavorite Answer
[ 1 ]
Foci S, S' ≡ ( ± ae, 0 ) ≡ ( ± 10, 0) ⇒ ae = 10 ... (1)
Co-vertices ≡ ( 0, ± b ) ≡ ( 0, ± 3 ) ⇒ b = 3 ....... (2)
∴ b² = a² ( 1 - e² ) ⇒ 9 = a² - a²e² ⇒ 9 = a² - (ae)²
∴ 9 = a² - 10² ∴ a² = 109
∴ a² = 109 and b² = 9
∴ ellipse : ( x² / 109 ) + ( y² / 9 ) = 1 ......... Ans.
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[ 2 ]
Foci S, S' ≡ ( 0, ± be ) ≡ ( 0, ± 8 ) ∴ be = 8 ....... (1)
Co-vertices ≡ ( ± a, 0 ) ≡ ( ≡ 20, 0 ) ∴ a = 20 .......(2)
But, ion this case, a² = b²( 1-e² )
∴ 400 = b² - (be)² ∴ 400 = b² - 8² ∴ b² = 464
∴ a² = 400, ... b² = 464
∴ ellipse : ( x² / 400 ) + ( y² / 464 ) = 1 ................. Ans.
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Happy To Help !
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