Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); Vertices: (0, -8), (0, 8)

Solution:

When the foci are on the y-axis the general equation of the ellipse is given by 

x² / b²  +  y² / a²   = 1  (a > b)

Center to focus distance c  = √(a² - b²)

Foci = (0, ±c)

Vertices = (0, ± a)

The given ellipse is as shown:

Foci = (0, ±2)

Vertices = (0, ± 8)

c = √(a² - b²)

2 = √(8² - b²)

Squaring both sides we get

4 = (64 - b²)

b² =  64 - 4 = 60

Hence the equation of the given ellipse is :

x²/60  +  y² /64  = 1  (a > b)

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); Vertices: (0, -8), (0, 8)

Summary:

The standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); Vertices: (0, -8), (0, 8) is x²/60  +  y² /64  = 1  .