Question

Find the polar form of circle with radius 2 and centre is (0,2)

Answer 1

To find polar form of circle , first of all we find certisian form of circle .
Given , radius = 2 and centre of circle = (0,2)
so, equation of circle : (x -0)² + (y - 2)² = 2²
⇒ x² + y² - 4y + 4 = 4
⇒ x² + y² - 4y = 0
Now put x = rcosФ and y = rsinФ
⇒ (rcosФ)² + (rsinФ)² - 4(rsinФ) = 0
⇒r²(cos²Ф + sin²Ф) - 4rsinФ = 0
⇒r² - 4rsinФ = 0 is the polar form of circle
Where r = √{x² + y²} and tanФ = y/x