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The detailed process of finding the position relationship between straight line and circle in high school mathematics
(1) center (1,-1), radius r=2√5.

Distance from center of circle to straight line d:

d = | k+ 1+ 1 |/√( 1+k? )

=|k+2|/√( 1+k? )& ltr

k? +2k+ 1 & lt; 20( 1+k? )

19k? -2k+ 19 & gt; 0

△= 4-4x 19x 19 & lt; 0

No matter what value k takes, the inequality holds, that is, D.

So both a straight line and a circle have two intersections.

(2) Chord length =2√(r? -Dee? )

=2√[20-(k? +2k+ 1)/( 1+k? )]

=2√[ 19-2k/( 1+k? )]

1+k? ≥2k k & gt; 0 means k= 1, and there is a minimum value.

The shortest chord length =2√ 18

=6√2