The equation

Question

The equation 4x^2+9y^2-36y = 0 defines a shifted ellipse. Write this equation in the standard form, find the center, focus, vertices of this ellipse, the lengths of major and minor axes and sketch the graph

Answer 1

You need to complete the square in the part of the equation that involves variable y.

 

 

4x² + 9(y² -4y .......) = 0

4x² + 9(y² - 4y + 4) = 36 ...added 4 within () on left side, but don't forget the outside factor 9, thus added 36 to right side

 

Now divide by 36 to get x²/9 + (y-2)²/4 = 1 ⇒ Center at (0,2), major axis runs parallel to x axis, a=3, b=2, etc.