A circle has a centre at the point [3, pi/2] in polar coordinates and a radius of 3. How do you find the equation of the circle in polar notation?

Question

7829 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-10T20:37:11

When given a polar point, #(r_0,phi)#, and a radius R.

The reference says that the equation of a circle in polar form is:

#r^2 - 2r_0cos(theta - phi)r + ro^2 = R^2#

Let's substitute the values for this problem:

#R = 3, r_0 = 3, and phi = pi/2#

#r^2 - 2(3)cos(theta - pi/2)r + 3^2 = 3^2#

#r^2 - 6cos(theta - pi/2)r = 0#

#r^2 = 6cos(theta - pi/2)r#

#r = 6sin(theta)#