ρ=2√5sinθ

Multiply both sides by p at the same time.

ρ? =2√5ρsinθ

∴x？ +y？ =2√5y (#)

x？ +(y-√5)？ =5

(2)

Parametric equation of straight line L, note that L passes through P(3, √5).

{ x = 3-√2/2 * t； y=√5-√2/2*t

Note that l passes through P(3, √5), M(x, y) is on l, and t=PM.

Replace (#) to get:

(3-√2/2t)？ +(√5-√2/2t)？ =2√5(√5-√2/2t)

Finishing:

t？ -3√2t+4=0

Let the parameter values corresponding to the intersection points A and B of a straight line L and a circle C be T 1 and T2, respectively.

Then t 1+T2 = 3 √ 2, t 1t2 = 4 > 0, t 1, T2 with the same sign.

|PA|=|t 1|，|PB|=|t2|

∴|pa|+|pb|=|t 1|+|t2|=|t 1+t2|=3√2