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Question

The radius of the circle with the polar equation r2-8r(3cosθ+sinθ)+15=0 is


A

8

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B

7

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C

6

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D

5

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Solution

The correct option is B

7


Solve for the radius of the circle.

r2-8r(3cosθ+sinθ)+15=0r2-8(3rcosθ+rsinθ)+15=0

wherercosθ=x,rsinθ=y

It can be rewritten in cartesian form as,

x2+y2-83x+y+15=0x2+y2-83x-8y+15=0

Now, radius

=432+42-15=0=48+16-15=7

Hence, option(B) is the correct answer.


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