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?

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Answer 1 · 2017-01-10T20:37:11

When given a polar point, $(r_{0}, ϕ)$ $(r_0,phi)$ , and a radius R.

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

$r^{2} - 2 r_{0} cos (θ - ϕ) r + r o^{2} = R^{2}$ $r^2 - 2r_0cos(theta - phi)r + ro^2 = R^2$

Let's substitute the values for this problem:

$R = 3, r_{0} = 3, and ϕ = \frac{π}{2}$ $R = 3, r_0 = 3, and phi = pi/2$

$r^{2} - 2 (3) cos (θ - \frac{π}{2}) r + 3^{2} = 3^{2}$ $r^2 - 2(3)cos(theta - pi/2)r + 3^2 = 3^2$

$r^{2} - 6 cos (θ - \frac{π}{2}) r = 0$ $r^2 - 6cos(theta - pi/2)r = 0$

$r^{2} = 6 cos (θ - \frac{π}{2}) r$ $r^2 = 6cos(theta - pi/2)r$

$r = 6 sin (θ)$ $r = 6sin(theta)$