Need help finding a bound for an equation

[jacksonjs20]

I'm trying to find a value K>o such that for real a,b,c,d

(a^2+c^2)x^2+2(ab+cd)xy+(b^2+d^2)y^2 ≤ K(x^2+y^2).

Any help on this would be greatly appreciated thanks.

 

[arildno]

Well, play a bit around using the fact that 2xy is always less than the sum of the two variables squared.

 

[jacksonjs20]

Thank you very much. I would have been stuck for hours.