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 1−x2144−y2256=−116−116×Equation 2
y281−y2256=19−116Add175y220736=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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