Question

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

Answer 1

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 $\frac{(x-h)^2}{a^2}+ \frac{(y-k)^2}{b^2}=1$.  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 $\frac{x^2}{64}+ \frac{y^2}{9}=1$