The equation of the circle whose diameter is the common chord of the circles
x 2 + y 2 + 3x + 2y + 1 = 0 and x 2 + y 2 + 3x + 4y + 2 = 0 is
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The equation of the common chord of the circles x 2 + y 2 + 3x + 2y + 1 = 0 and x 2 + y 2 + 3x + 4y + 2 = 0 is 2y + 1 = 0. (Using S 1 -S 2 = 0)
The equation of a circle passing through the intersection of
x 2 +y 2 +3x+2y+1 = 0 and x 2 +y 2 +3x+4y+2 = 0 is
(x 2 +y 2 +3x+2y+1) + λ λ (x 2 +y 2 +3x+4y+2) = 0
⇒ ⇒ x 2 +y 2 +x 
.… (1)
Since 2y + 1 = 0 is a diameter of this circle, therefore its centre 
lies on 2y + 1 = 0 i.e. -2 
⇒ ⇒ -4 λ λ - 2 + λ λ +1 = 0 ⇒ ⇒ - 3 λ λ = 1 ⇒ ⇒ λ λ = – 
.
Putting λ λ = – 
in (1), the equation of the required circle is 2x 2 +2y 2 +6x+2y+1 = 0
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