Graphing & standard equation

Question

The general form of the equation of an ellipse is (9x^2) + (4y^2) + 54x - 8y + 49=0. Write the equation of this ellipse in standard form and give the coordinates of the center, the length of the major axis, and the length of the minor axis. Then graph the ellipse 

Answer 1

9(x²+6x) + 4(y²-2y) = -49

 

Completing the square for the x terms and for the y terms, we get:

 

9(x² + 6x + 9 - 9) + 4(y² - 2y + 1 - 1) = -49

 

9(x + 3)² - 81 + 4(y - 1)² - 4 = -49

 

9(x + 3)² + 4(y - 1)² = 36

 

(x + 3)²/4 + (y - 1)²/9 = 1

 

Center = (-3, 1)

 

a² = 9    b² = 4

 

Length of (vertical) major axis = 2a = 6

Length of (horizontal) minor axis = 2b = 4