Plotting ellipses: 36x^2+9y^2-216x=0?

Question

What are the steps in putting the above equation into the equation for an ellipses?

Answer 1

First thing to do is complete squares:

36x^2 - 216x + 9y^2 = 0

36x^2 - 36*2*3x + 36*9 - 36*9 + 9y^2 = 0

36(x^2 -2*3x +9) - 324 + 9y^2 = 0

36(x - 3)^2 + 9y^2 = 324 // divide by 324

[(x-3)^2 ]/9 + (y^2)/36 = 1


This is the form of the equation of an elipse.

Answer 2

Take the given equation for an ellipse and put it into standard form by completing the square.

36x² + 9y² - 216x = 0
36(x² - 6x + 9) + 9y² = 0 + 36*9
36(x - 3)² + 9y² = 324

Divide thru by 324.

(x - 3)²/9 + y²/36 = 1

The equation is now in standard form for an ellipse.
The ellipse has center (3,0).
Semi-major axis is √36 = 6
Semi-minor axis is √9 = 3

Answer 3

Strange question for the medicine section.