# Thread: anyone who can help me with this problem:

1. ## anyone who can help me with this problem:

find the length of the chord 3x-y+9=0
of the circle x^2+y^2=5

2. One can see a very dull method here.

Solve the two equations for the points of intersection,

$y=3x+9$

$x^2+y^2=5$

Therefore,

$x^2 + 9(x+3)^2=5$

$10x^2 + 54x+81=5$

$5x^2+27x+38=0$

so discriminant of this equation=729-760< 0

i.e. the line doesn't meet the given circle at all

$\left\{\begin{array}{ll}x^2+y^2=5\\3x-y+9=0\end{array}\right.$
From the second ecuation $y=3x+9$. Replace y in the first equation. We get the quadratic
$5x^2+27x+38=0$
But the discriminant is $\Delta =-31<0$, so the system has no real solution. That means the line doesn't intersect the circle.