Yahoo Answers is shutting down on 4 May 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
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 agoFavourite 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.
..........................................................................................
[ 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.
...........................................................................................
Happy To Help !
...........................................................................................
