Find the radius of the circle with the polar equation `r^2-8r(sqrt3costheta+sintheta+15=0`

Options

A. 8
B. 7
C. 6
D. 5

Answer

B

Explanation

Given , ` r ^ 2 - 8 ( sqrt 3 r cos theta + r sin theta ) + 15 = 0 `
where ` r cos theta = x and y = r sin theta `
It can be rewritten in cartesian form as
` x ^ 2 + y ^ 2 - 8 ( sqrt 3 x + y ) + 15 = 0 `
` rArr x ^ 2 + y ^ 2 - 8 sqrt 3 x - 8 y + 15 = 0 `
Now, radius ` = sqrt (( 4 sqrt3 ) ^ 2 + (4) ^ 2 - 15 ) = 7 `