Find the center, vertices, and foci for the ellipse 25x^2+64y^2=1600

Step-by-step explanation:

Answer:

Data

Equation 25x² + 64y² = 1600

Process

1. - Divide all the equation by 1600

25x²/1600 + 64y² / 1600 = 1600/1600

-Simplify

x²/64 + y² / 25 = 1

2. - Equation of a horizontal ellipse

3. - Find a, b and c

a² = 64 a = 8

b² = 25 b = 5

-Calculate c with the Pythagorean theorem

a² = b² + c²

-Solve for c

c² = a² - b²

-Substitution

c² = 8² - 5²

-Simplification

c² = 64 - 25

c² = 39

-Result

c = √13

4. - Find the center

C = (0, 0)

5. - Find the vertices

V1 = (-8, 0) V2 = (8, 0)

6. - Find the foci

F1 = (-√13, 0) F2 = (√13, 0)

Answer: A

Step-by-step explanation: Center (0,0)

Vertices (+/-8,0)

Foci (+/-6.2,0)