Determine the equation of the ellipse whose graph is given below.
The form x2b2+y2a2=1 is an ellipse with vertical major axis and whose vertices are
(0,±a). Notice from the graph that b=2 and the ellipse pass through points (−1,2) which means that the point is a solution on the ellipse.
So, by substitution
(−1)222+22a2=114+4a2=1Subtract 144a2=34Apply cross multiplication3a2=16Solve for aa=4√3
Thus, the equation is
x222+y2(4√3)2=1Orx24+y2163=1x24+3y216=1
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