Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -6), (0, 6); Vertices: (0, -8), (0, 8)

Solution:

When the focii 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, ±6)

Vertices = (0, ± 8)

c = √(a² - b²)

6 = √(8² - b²)

Squaring both sides we get

36 = (64 - b²)

b² = 64 - 36 = 28

Hence the equation of the given ellipse is :

x²/ 28 + y² /64 = 1 (a > b)

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -6), (0, 6); Vertices: (0, -8), (0, 8)

Summary:

The standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -6), (0, 6); Vertices: (0, -8), (0, 8) is x²/ 28 + y² /64 = 1