Question

Write the equation of each ellipse in standard form with the given characteristics.

Answer 1

Answer:

Step-by-step explanation:

The foci are horizontally aligned.

horizontal ellipse:

(x-h)²/a² + (y-k)²/b² = 1

center (h,k)

vertices (h±a,k)

length of minor axis = 2b

foci (h±c,k), c² = a²-b²

Apply your data and solve for h, k, a, and b.

foci (±3√19, 6)

h = 0

k = 6

Length of minor axis = 2b = 10

b = 5

foci (h±3√19, 6)

c = 3√19

c³ = a² - b²

171 = a² - 25

a²  = 196

x²/196 + (y-6)²/25 = 1