The Point $( 1 , - 2 )$ Is the Midpoint of a Chord of the Circle

Multiple Choice

The point $( 1 , - 2 )$ is the midpoint of a chord of the circle $x ^ { 2 } - 4 x + y ^ { 2 } + 2 y = 8$ . Find the length of the chord.

A) $4 \sqrt { 11 }$
B) $\sqrt { 22 }$
C) $22$
D) $11 \sqrt { 2 }$
E) $2 \sqrt { 11 }$