Find the center, vertices, and foci of the ellipse with the equation [tex]5x^2 + 8y^2 = 40[/tex].

for an ellipse x²/a² + y²/a² = 1 vertices are -a,0 a, 0 0,b 0, -b focus : √(a²-b²) , 0 center is origin 0,0
given ellipse : divide by 40 on both sides
x² / 8 + y²/5 = 1 **So a = √8 = 2√2 b = √5 **
vertices are -2√2,0 2√2,0 0,√5 0,-√5 focii = √3, 0 -√3, 0

Answered by Everest2017 | 2024-06-10

Center of the ellipse = (0, 0)
vertices are **(±√8, 0) and ** (0, ±√5)
Focus of the ellipse = (±√3, 0) . ;

Answered by eudora | 2024-06-12

The center of the ellipse is at (0, 0). The vertices are (2√2, 0), (-2√2, 0), (0, √5), and (0, -√5), while the foci are at (√3, 0) and (-√3, 0).
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Answered by Everest2017 | 2024-10-30