I have a problem for which I am given a choice of 4 answers:
hyperbola (angle of rotation 45 degrees)
ellips (angle of rotation 90 degrees)
hyperbola (angle of rotation 60 degrees)
ellipse (angle of rotation 30 degrees)
The problem: Identify the conic from the equation 13x^2-6(sq.rt. 6)xy+7y^2-16=0.
I used the discriminant (-148) is less than 0 and A does not equal C. Therefore, this is the equation of an ellipse.
I am using the formula tan2theta = B/A-C to find the angle of rotation.
tan 2theta = -6(sq.rt. 6)/13-7 or -6(sq.rt.6)/6 = -(sq.rt.6)
tan 2theta=-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!