The first question, ρ is p 1M or point p? First, the coordinate of point A is (p/cosi-pcota, 0.

Connect OMa to point a coordinates.

Trigonometric function relation

a=θ+∠AMO？ ρ/sin(pi-a)=a/sin(a-i)

the second question

set up

Center M(ρ, θ)? Radius r? Pole o

Any point on the circle P(ρ, θ)

δδOPM

According to cosine theorem

|om|^2+|op|^2-2|om|*|op|*cos(θ-θ')=|pm|^2

(ρ')^2+ρ^2-2ρρ'cos(θ-θ')=r^2