Sunday, May 19, 2019

College Algebra, Chapter 8, 8.2, Section 8.2, Problem 28

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=43


Thus, the equation is

x222+y2(43)2=1Orx24+y2163=1x24+3y216=1

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