Find the length of the common chord of the parabola `x^2=4(x+3)` and the circle `x^2+y^2+4x=0` .

Answer

4

Explanation

Solving given equations, we have
`-x^(2)-4x=4x+12`
`rArr" "x^(2)+8x+12=0`
`rArr" "x=-2,(x=-6` is not possible)
From equation of parabola,
`y^(2)=4(-2+3)=4`
`:." "y=pm2`.
So, curves intersect at (-2,2) and (-2,-2).
So, length of common chord is 4.