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

Answer:

The answer to your question is

Standard form

        $\frac{(x - 6)^{2} }{12^{2}} + \frac{(y - 3)^{2} }{20^{2}} = 1$

General form

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

Step-by-step explanation:

Data

Vertical ellipse

Mayor axis = a = 20

Minor axis = b = 12

Center = (6, 3)

Formula

              $\frac{(x - h)^{2} }{b^{2}} + \frac{(y - k)^{2} }{a^{2}} = 1$

Substitution and standard form

              $\frac{(x - 6)^{2} }{12^{2}} + \frac{(y - 3)^{2} }{20^{2}} = 1$

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