x2+2xy+y2+2x+2y-5 = 0 ...(1)
3xy+1 = 0
⇒ y - 3x = 1 ...(2)
Let A and B the point of intersection.
Homogenising (1) with the help of (2), combined eq. of OA and OB is
x2 + 3xy + y2 + 2x(y - 3x) + 2y(y - 3x) - 5(y - 3x)2 = 0
On solving
-50x2 + 28xy - 2y2 = 0
as 25x2 - 14xy + y2 = 0
cosθ \(=\left|\frac{25+1}{\sqrt{(25-1)^2+196}}\right|=\left|\frac{26}{\sqrt{772}}\right|=\frac{13}{\sqrt{193}}\)
θ = cos-1\((\frac{13}{\sqrt{193}})\)