First, we can know that the coordinates of the center of the circle (2cosθ, 2-2cos2θ) are, and then according to the relationship between the coordinates, cos2θ=2cos? θ- 1 can get the locus of the center of the circle 2-2cos2θ=2-4cos? θ+2=-4cos？ θ+4=-(2cosθ)？ +4 So if the center of the circle is (x, y), the trajectory is.

y=-x？ +4 This is the first question. You can try the next one yourself.

In the first question of the second question, the linear equation is transformed into the normal function ρ sin (θ-π/4) y = ρ sin θ cos π/4 = ycos π/4-xsin π/4 = 2 (-1/2) (y-x) = m, that is, in the.