Answer:
The answer to your question is
Standard form
[tex]\frac{(x - 6)^{2} }{12^{2}} + \frac{(y - 3)^{2} }{20^{2}} = 1[/tex]
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
[tex]\frac{(x - h)^{2} }{b^{2}} + \frac{(y - k)^{2} }{a^{2}} = 1[/tex]
Substitution and standard form
[tex]\frac{(x - 6)^{2} }{12^{2}} + \frac{(y - 3)^{2} }{20^{2}} = 1[/tex]
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
