Polar Coordinates Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
Convert the equation x2+y2=6xx^2 + y^2 = 6x to polar form.

Solution

  1. 1
    Substitute x2+y2=r2x^2 + y^2 = r^2 and x=rcos⁡θx = r\cos\theta: r2=6rcos⁡θr^2 = 6r\cos\theta.
  2. 2
    Divide both sides by rr (for r≠0r \neq 0): r=6cos⁡θr = 6\cos\theta.

Answer

r=6cos⁡θr = 6\cos\theta
The substitutions x=rcos⁡θx = r\cos\theta, y=rsin⁡θy = r\sin\theta, and x2+y2=r2x^2 + y^2 = r^2 convert rectangular equations to polar form. The equation r=6cos⁡θr = 6\cos\theta represents a circle of radius 3 centered at (3,0)(3, 0) in rectangular coordinates.

About Polar Coordinates

A coordinate system where each point in the plane is described by a distance rr from the origin and an angle θ\theta from the positive xx-axis, written as (r,θ)(r, \theta).

Learn more about Polar Coordinates →

More Polar Coordinates Examples

Example 1 easy

Convert the polar coordinates [formula] to rectangular (Cartesian) coordinates.

Example 2 medium

Convert the rectangular point [formula] to polar coordinates with [formula] and [formula].

Example 4 hard

Find all polar representations of the point with rectangular coordinates [formula] where [formula].

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