Question

Write the equation of a vertical ellipse with a major axis of 20, a minor axis of 12, and a center of (6, 3)

Answer 1

The answer to your question is

Standard form

`((x - 6)^(2) )/(12^(2)) + ((y - 3)^(2) )/(20^(2)) = 1`

General form

400x² + 144y² - 4800x - 864y - 41904 = 0

Explanation:

Data

Vertical ellipse

Mayor axis = a = 20

Minor axis = b = 12

Center = (6, 3)

Formula

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

Substitution and standard form

`((x - 6)^(2) )/(12^(2)) + ((y - 3)^(2) )/(20^(2)) = 1`

General equation

400(x - 6)² + 144(y - 3)² = 57600

400(x² - 12x + 36) + 144(y² - 6y + 9)² = 57600

400x² - 4800x + 14400 + 144y² - 864y + 1296 = 57600

400x² + 144y² - 4800x - 864y +14400 + 1296 - 57600 = 0

400x² + 144y² - 4800x - 864y - 41904 = 0