Right in equation of the ellipse the rest of the question is in the photo

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

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.