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Chapter 10: Q. 9 (page 701)

Find a polar equation for the circle with center at the point (0,4)and radius 4. Graph this circle.

Short Answer

Expert verified

The equation is r=8sin胃and the graph is

Step by step solution

01

Step 1. Given Information 

The given center is(0,4)and radius is 4.

02

Step 2. Explanation 

The equation has a circle in rectangular cartesian coordinates is given below,

(x-h)2+(y-k)2=a2

The circle has a radius 4 units and center at (0,4),

(x-0)2+(y-4)2=42x2+y2-8y=0

Thus, equation of circle in rectangular coordinates is x2+y2-8y=0

Substitute the values x=rcos胃,y=rsin胃to get the polar form of the equation.

(rcos胃)2+(rsin胃)2-8(rsin胃)=0r2-8rsin胃=0r=8sin胃

And the graph is as follows,

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