( 1)
cosα=x+ 1,sinα=y
Because? α+sin? α= 1
(x+ 1)? +y? = 1
Center coordinate (-1, 0), radius = 1.
Curve C 1 is a circle with (-1, 0) as the center and 1 as the radius.
ρ(cosθ+ksinθ)=-2
ρcosθ+k ρsinθ+2=0
x+ky+2=0
Distance formula from the center of a point to a straight line to a straight line:
d=|- 1+k 0+2|/√( 1+k? )= 1/√( 1+k? )
When k=0, d= 1= circle radius, and the curve C 1 is tangent to the straight line L.
When k≠0, k? & gt0,√( 1+k? )& gt 1, 1/√( 1+k? )& lt 1
D< 1, curve C 1 intersects with straight line L.
(2)
A straight line intersects a circle, k≠0
x+ky+2=0
ky=-x-2
y=(- 1/k)x - 2/k
The slope of the straight line is-1/k.
Half the chord length AB, the distance from the center of the circle to the straight line and the radius of the circle form a right triangle.
d? +(AB/2)? =r?
d= 1/√( 1+k? ), AB=√2, r= 1, sort, get.
k? = 1
K= 1 or k=- 1.
When k= 1,-1/k =-11=-1; When k=- 1,-1/k =-1(-1) =1.
The slope of the straight line L is 1 or-1.