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