Question

(a) Find an orthogonal matrix which will transform the quadratic form Q=5x^2 +8y^2 -4xy into sum of squares
(b) Reduce the conic 5x^2 +8y^2 -4xy -36 = 0 into standard form (sum of squares) and sketch the conic.

Answer 1

for b, group like terms (get all the x's together and all the y's together).

Answer 2

I'm trying to remember how to do part. a. Lol But I think you use the 1,0,0: 0,1,0, 0,0,1 matrix set to find it's orthogonality.