Simplifying the Equation for a Circle: r2 = 20 - 4θ + 10θ2

[Lurid]

Homework Statement

Eliminate the parameter:

x=2-3θ
y= 4+θ

Homework Equations

x² + y² = r²

The Attempt at a Solution

[x=2-3θ]²; [y= 4+θ]²

x²= 4-12θ+9θ²
y²= 16+8θ+θ²
-------------------------------------
x²+y² = 20 - 4θ + 10θ²

r² = 20 - 4θ + 10θ²

Is there another step that I can take to simplify this expression further?

 

[Filip Larsen]

From the statement "eliminate the parameter", and assuming the parameter is θ, I would more expect you would have to establish a direct relation between x and y (that is, eliminate θ from the two equations to form one equation involving only x and y).