Problem: Identify the conic from the equation 13x^2-6(sq.rt.6)xy+7y^2-16=0

Question

I have to choose from the following four answers:

hyperbola (angle of rotation 45)
hyperbla (angle of rotation 60)
ellipse (angle of rotation 90)
ellipse (angle of rotation 30)

I used the discriminant (-148) is less than 0--equation on an ellipse and A does not equal C.

I am using the formula tan2theta=B/A-C to find the angle of rotation.
tan2theta = -6(dq.ft.6)/13-7 = -6(sq.rt.6)/6 =-(sq.rt. 6)
tan2theta=-67.79
theta=-33.89 degrees

Where have I gone wrong finding the angle of rotation? I have my calculator set to degrees.

Thanks for helping!

Answer 1

Using
Theta = 0.5 arccot((a-c)/2/b)
Theta= 1/2 arccot((6/2)/6sqrt6
=1/2 arccot(1/2sqrt6)

I get slightly less than 40 deg

Answer 2

Ellipse -34