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Chapter 9: Q.85 (page 585)

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

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

coordinates.

Short Answer

Expert verified

(x-a)2+y2=a2

Step by step solution

01

Step 1. Given

given polar coordinate

r=2acos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=2ax

03

Step 3. Calculation

Consider the given polar coordinate

r=2acos胃multiplytheaboveequationbyrr2=2a.rcos胃substitutex2+y2inplaceofr2andrcos胃forxwegetx2+y2=2axx2+y2-2ax=0Nowadda2bothsidestomakeitaperfectsquarey2+(x2-2ax+a2)=a2y2+(x-a)2=a2whichisoftheformofequationofacircle.

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Most popular questions from this chapter

In Problems55鈥�66, the rectangular coordinates of a point are given. Find polar coordinates for each point.

0,2

Identify and graph each polar equation. Verify your graph using a graphing utility.

r=2+2cos胃

Identify and graph each polar equation. Verify your graph using a graphing utility

r=3-3sin胃

In Problems, the vector v has initial point P and terminal point Q. Write v in the form ai + bj; that is, find its position vector.

P=3,2;Q=5,6

In Problems 39鈥�54, the polar coordinates of a point are given. Find the rectangular coordinates of each point.

(6.3,3.8)
See all solutions

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