Tuesday, October 23, 2018

College Algebra, Chapter 8, 8.2, Section 8.2, Problem 46

Determine the parts of intersection of the pair of ellipses.

{x216+y29=1x29+y216=1

Sketch the graphs on the same axes and label the points of intersection.
By using elimination method,

{x2144+y281=1919×Equation 1x2144y2256=116116×Equation 2


y281y2256=19116Add175y220736=7144Simplifyy=±125=±2.4

Now we back substitute the value of y in either of the equation. So if y=±125, then

x216+(±125)29=1x=±125=±2.4

Therefore, the parts of intersections are (2.4,2.4),(2.4,2.4),(2.4,2.4) and (2.4,2.4)

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