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Chapter 9: Q. 55 (page 775)

Prove Theorem 9.16 (b). That is, show that if 0<A<B, the graph of the curve with equationrole="math" localid="1663152551040" x2A2+y2B2=1 is an ellipse with foci role="math" localid="1663154443592" 0,卤B2-A2.

Short Answer

Expert verified

Hence, proved.

Step by step solution

01

Given information.

The equation of the ellipse is x2A2+y2B2=1

02

Plot the graph.

The graph of the ellipse x2A2+y2B2=1is,

The vertices of the parabola are 0,卤B2-A2

And, from the graph it is observed that the foci of the parabola is the same 0,卤B2-A2.

Hence, proved.

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