Write the equation of an ellipse with a major axis of length 8 and co-vertices (0, 3) and (0, -3).

Question

thats it 

Answer 1

The major axis is the x-axis.  The co-vertices indicate the length of the minor axis, which is 6.  Since the co-vertices have an x-coordinate of 0, the centerpoint of the ellipse is (0, 0).

 

If the length of the major axis is 8, then the coordinates left and right endpoints of the ellipse is (-4, 0) and (4, 0).

 

The equation of the ellipse is then

 

(x² / 4²) + (y² / 3²) = 1

 

 

Multiply both sides of the equation of the LCD.  LCD is 144.

 

9x² + 16y² = 144