Question

Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 10.

A. x squared divided by 5 plus y squared divided by 8 = 1
B. x squared divided by 25 plus y squared divided by 64 = 1
C. x squared divided by 8 plus y squared divided by 5 = 1
D. x squared divided by 64 plus y squared divided by 25 = 1

Answer 1

The answer to your question is the letter B.

Explanation:

Data

major axis = 16

minor axis = 10

Process

1.- Calculate the value of a

major axis = 2a = 16

a = 16/2

a = 8

2.- Calculate the value of b

minor axis =2b = 10

b = 10/2

b = 5

3.- Write the equation of a vertical ellipse

`((x - h)^(2))/(b^(2)) + ((y - k)^(2))/(a^(2)) = 1`

C = (0, 0) and h = 0, k= 0

4.- Write the equation of the ellipse

`(x^(2))/(5^(2)) + (y^(2))/(8^(2)) = 1`

The right answer is B because the denominators are simplified.