11.2k views
3 votes
Write the equation of an ellipse with a major axis of length 8 and co-vertices (0,3) and (0,-3)

1 Answer

2 votes
If the co-vertices are (0, 3) and (0, -3) where x is 0 and y has a value, then y is the minor axis. That means that the x axis is the major axis. Because of what the co-vertices are, the center of the ellipse is at the origin. The formula for an ellipse that has a horizontal major axis is
((x-h)^2)/(a^2)+ ((y-k)^2)/(b^2)=1. The a value will always be larger than the b value, therefore, the a value goes under the coordinate that is the major axis. Here, its the x-axis. a is the distance that the outer edge of the ellipse is from the center. It's 8 units away from the center along the x axis and 3 units along the y axis from the center. So a = 8 and a^2 = 64; b = 3 and b^2 = 9. Our formula then is
(x^2)/(64)+ (y^2)/(9)=1
User Leonida
by
6.2k points