Convert the equation 2x2 2y2 8y 0 into polar form a r 4

Convert the equation 2x^2 + 2y^2 - 8y = 0 into polar form. a) r = 4 b) r = 4 sin(theta) c) r = 4 cos(theta) d) r = 2 sin(theta) e) r = 2 cos(theta) f) None of the above

Solution

Option b) is correct.

Given

2x^2 + 2y^2 - 8y = 0

Let x = R*cos t, y = R*sin t and x^2 + y^2 = R^2

Then 2R^2 - 8Rsin t = 0

2R(R - 4*sin t) = 0

R = 0

and R = 4*sint