Let Z distance 기 be d₂ Point on ellipse between z and I d₁ = and distance = a (Z-1) (2-1) between z √ (Z+1) (2+1) As Point i so == -1 Ад I and -1 are foci of ellipse and Point on ellipse then by defination d₁ + d₂ = c (constant) √ (z-1) (1) + √ (z+1) (2+1) ZZ-Z-Z +1 is then is di 기 C= 2√2 So equation of ellipse and -1 √1-² +² +1 +√1+i-i+1 i Squaring both sides ZZ + Z + € +1 zz-z-Z+1 +√ZZ+Z+ = +1 = 2 6ZZ-Z²-Z² = 8 ²- 7² = 8 с on the ellipse so that Put z= i and ZZ = 1 is d₂ so that = c then = C = z be a = 2√√/2 2 (Z²+ 1) + 2 √(z{+1)³²_ (Z+Z) ² (zz71) 2 (2+z) 2 ZZ-3 Again Squeasing both sides 2 (ZZ-3)² = (2+1)²2²_ (Z+Z)² (zz)2+9 - 6zz (zē)²+1+2zz-(Z)²_ (€) ²³-277 8
Let Z distance 기 be d₂ Point on ellipse between z and I d₁ = and distance = a (Z-1) (2-1) between z √ (Z+1) (2+1) As Point i so == -1 Ад I and -1 are foci of ellipse and Point on ellipse then by defination d₁ + d₂ = c (constant) √ (z-1) (1) + √ (z+1) (2+1) ZZ-Z-Z +1 is then is di 기 C= 2√2 So equation of ellipse and -1 √1-² +² +1 +√1+i-i+1 i Squaring both sides ZZ + Z + € +1 zz-z-Z+1 +√ZZ+Z+ = +1 = 2 6ZZ-Z²-Z² = 8 ²- 7² = 8 с on the ellipse so that Put z= i and ZZ = 1 is d₂ so that = c then = C = z be a = 2√√/2 2 (Z²+ 1) + 2 √(z{+1)³²_ (Z+Z) ² (zz71) 2 (2+z) 2 ZZ-3 Again Squeasing both sides 2 (ZZ-3)² = (2+1)²2²_ (Z+Z)² (zz)2+9 - 6zz (zē)²+1+2zz-(Z)²_ (€) ²³-277 8
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter7: Conic Sections And Quadratic Systems
Section7.2: The Ellipse
Problem 69E
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