Given: equations of the circles are x2+y2+2x+3y+1=0 and x2+y2+4x+3y+2=0 S1:x2+y2+2x+3y+1=0 .... (1) S2:x2+y2+4x+3y+2=0 .... (2) Now the equation of the common chord is S1−S2=0 ⇒(x2+y2+2x+3y+1)−(x2+y2+4x+3y+2)=0 ⇒−2x−1=0 ∴x=
−1
2
Put the value of x in equation (1), we get ⇒(
−1
2
)2+y2+2×(
−1
2
)+3y+1=0 ⇒
1
4
+y2−1+3y+1=0 ⇒y2+3y+
1
4
=0⇒4y2+12y+1=0 ⇒y=
−12±√122−4×4×1
2×4
=
−12±√128
8
⇒y=
−12±8√2
8
=
−3
2
±√2 Intersection points of the chord are (
−1
2
,
−3
2
+√2)‌and(
−1
2
,
−3
2
−√2)
Now the length of the common chord of the circles = Distance between Intersection points