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Chapter 12: Q. 9 (page 840)

Find the polar equation of a circle with center at 0,4that passes through the pole. What is the rectangular equation?

Short Answer

Expert verified

The polar equation of the circle is x2+y2-8y=0and rectangular equation isr-8sin胃=0.

Step by step solution

01

Step 1. Given Information

Centre of the circle is 0,4that passes through the pole. This means that radius is 4.

We need to find the equation of circle.

02

Step 2. Finding Equation of circle

x-h2+y-k2=r2x-02+y-42=42x2+y2+16-8y=16x2+y2-8y=0

03

Step 3. Rectangular Equation

Put x=rcos胃,y=rsin胃

x2+y2-8y=0r2-8rsin胃=0rr-8sin胃=0r-8sin胃=0

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