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Chapter 9: Q. 83 (page 584)

Show that the graph of the equation r=2asin胃, a>0,

is a circle of radius a with center at (0,a)in rectangular

coordinates.

Short Answer

Expert verified

x2+(y-a)2=a2

Step by step solution

01

Step 1. Given

given polar coordinate

r=2asin胃

02

Step 2. Concept

To convert given polar coordinate into rectangular coordinate we try to deduce the given polar coordinate into the following expression:

x2+y2=2ay

03

Step 3. Calculation

Consider the given polar coordinate

r=2asin胃multiplytheaboveequationbyrr2=2a.rsin胃substitutex2+y2inplaceofr2andrsin胃forywegetx2+y2=2ayx2+y2-2ay=0Nowadda2bothsidestomakeitaperfectsquarex2+(y2-2ay+a2)=a2x2+(y-a)2=a2 whichisoftheformofequationofacircle.

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Most popular questions from this chapter

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