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Answer:
1) The vertices are (-5 , 0) and (5 , 0)
The co-vertices are (0 , -2) and (0 , 2)
The foci are (-√21 , 0) and (√21 , 0)
2) The equation of the ellipse ⇒ x²/48 + y²/64 = 1
Step-by-step explanation:
1) ∵ 4x² + 25y² = 100 ⇒ ÷ 100
∴ x²/25 + y²/4 = 1
∵ The standard equation of the ellipse with center (0 , 0) is
x²/a² + y²/b² = 1
∴ a² = 25 ⇒ ∴ a = ±5
∴ The vertices are (-5 , 0) and (5 , 0)
∴ b² = 4 ⇒ ∴ b = ±2
∴ The co-vertices are (0 , -2) and (0 , 2)
∵ c² = a² - b²
∴ c² = 25 - 4 = 21
∴ c = ±√21
∴ The foci are (-√21 , 0) and (√21 , 0)
2) ∵ Its center is (0 , 0)
∵ The vertex of it is (0 , -8)
∴ a² = 64
∵ The focus is (0 , 4)
∴ c² = 16
∵ c² = a² - b²
∴ b² = a² - c² = 64 - 16 = 48
∵ b² = 48
The standard equation of the ellipse with center (0 , 0) is
x²/b² + y²/a² = 1 ⇒ major axis // to y-axis
∴ x²/48 + y²/64 = 1
