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Chapter 9: Q. 84 (page 584)

Show that the graph of the equation r=-2asin胃, ,

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=a2whichisoftheformofequationofacircle.

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Most popular questions from this chapter

If the rectangular coordinates of a point are 4,-6,the point symmetric to it with respect to the origin is ______.

The standard equation of a circle with center at -2,5and radius 3is ______ .

To test if the graph of a polar equation may be symmetric with respect to the polar axis, replace 胃by ________.

Find zw and zw. Leave the answers in polar form.

z=1-iw=1-3i

True or False A cardiod passes through the pole.
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