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