This kind of problem, if you are not familiar with polar coordinates, must be transformed into rectangular coordinates to solve, and the topic also requires equations of rectangular coordinates.

ρ= 1 is a circle with the origin (pole) as the center and the radius of 1, and the corresponding rectangular coordinate equation is x? +y？ = 1;

The rectangular coordinates of n are x=√2cos(π/4)= 1, y=√2sin(π/4)= 1, n (1,1);

(I) let M(xm, ym), xm? +ym？ = 1, g coordinate (x, y), according to the relationship between vector addition and coordinates:

x=xm+ 1，y = ym+ 1； xm=x- 1，ym = y- 1； Substitute into the above formula:

(x- 1)？ +(y- 1)？ = 1, this is the C2 equation of G, and it is also a circle with the center of N( 1, 1) and the radius of 1!

(2) In this parametric equation, t is the distance from the point with coordinates (x, y) on a straight line to p (2,0), and this distance is directional (positive and negative). According to the second formula, y is directly proportional to t, so the y-axis component and y-axis of t can be defined as positive direction (upward).

So |PA|=|t 1|, |PB|=|t2|

|PN|=√[(2- 1)？ +(0- 1)? ]=√2 & gt； 1, ∴P is outside the circle, n, PA and PB are in the same direction, and t 1 is the same sign as t2.

Substitute the parameter equation into the trajectory equation of C2:

(2-t/2- 1)？ +(t√3/2- 1)？ = 1

( 1-t/2)？ +(t√3/2- 1)？ = 1

1-t+t？ /4+3t？ /4-t√3+ 1= 1

t？ -( 1+√3)t+ 1=0

According to Vieta's theorem:

t 1+t2= 1+√3

t 1t2= 1

It can be seen that t 1 and t2 are both positive numbers.

1/|PA|+ 1/|PB|

= 1/t 1+ 1/t2

=(t 1+t2)/(t 1t2)

= 1+√3