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