Question

Find an equation for the ellipse that satisfies the given conditions.

Endpoints of minor axis (0, ±3), distance between foci 8

Answer 1

Ok remember the general equation for an ellipse is:\[x ^{2}/a ^{2}+y ^{2}/b ^{2}=1\] with center at the origin. The constant a represents the longest length or major axis. And the formula to calculate the focus is\[c ^{2}=a ^{2}-b ^{2}\] where c is the distant from origin to the focus. With this in mind, if the endpoint for the minor axis is (0,3) then \[b=3\rightarrow b ^{2}=9\] Now to calculate \[a\] we use the formula for the focus:\[c ^{2}=a ^{2}-b ^{2}\rightarrow 8^{2}= a ^{2}-3^{2}\rightarrow a ^{2}= 64+9=73\] Therefore the formula is given:\[x ^{2}/73+ y ^{2}/9 =1\] Peace, Love and Happiness from Puerto Rico