( 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.