What Are the Boundaries of θ and r for a Circle Centered at (1,2)?

[Jonmundsson]

Homework Statement

We have the circle [itex](x - 1)^2 + (y-2)^2 = 1[/itex]. Find the boundaries of θ and r.

Homework Equations

x = h + rcosθ
y = k + rsinθ

The Attempt at a Solution

This is a circle with its origin at (1,2) and a radius of 1 so r is between 0 and 1 and the circle lies in the first quadrant but touches the x and y-axis so theta is between 0 and pi/2

Is this correct? Just curious

edit: additional question: let's say I define y = 2 + rsinθ and x = 1 + rcosθ. Would this circle go from 0 to 2pi? (point of origin (1,2))

 

[LCKurtz]

Homework Statement

We have the circle [itex](x - 1)^2 + (y-2)^2 = 1[/itex]. Find the boundaries of θ and r.

Homework Equations

x = h + rcosθ
y = k + rsinθ

The Attempt at a Solution

This is a circle with its origin at (1,2) and a radius of 1 so r is between 0 and 1 and the circle lies in the first quadrant but touches the x and y-axis so theta is between 0 and pi/2

Is this correct? Just curious

edit: additional question: let's say I define y = 2 + rsinθ and x = 1 + rcosθ. Would this circle go from 0 to 2pi? (point of origin (1,2))

Your comment in the edit is exactly how to set up the problem. You would put ##r = 1## to get the circle and ##0 \le r \le 1## to get the interior.