If length of the common chord of the circles `x^2 + y^2 + 2x + 3y + 1 = 0 and x^2 + y^2 + 4x + 3y + 2 = 0` then the value of `[a].` (where [ - ] denotes greatest integer function)

Options

A. `(9)/(2)`
B. `2sqrt(2)`
C. `3sqrt(2)`
D. `(3)/(2)`

Answer

B

Explanation

The centres of the circle are `C_(1)(-1,-3//2) and C_(2)(-2, -3//2)` and corresponding radii are `r_(1)sqrt(1+(9)/(4)-1=(3)/(2)) and r_(2)=sqrt(4+(9)/(4)-2)=(sqrt(17))/(2)` respectively.
The equation of the common chord is 2x+1=0

`:. C_(1)M=|(-2+1)/(sqrt(2^(2) +0^(2)))|=(1)/(2)`
Hence, PQ`=2PM=2sqrt(C_(1)P^(2)-C_(1)M^(2))=2sqrt((9)/(4)-(1)/(4))=2sqrt(2)`