Posted by Joanie on .
Problem: Identify the conic from the equation 13x^26(sq.rt.6)xy+7y^216=0
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 0equation on an ellipse and A does not equal C.
I am using the formula tan2theta=B/AC to find the angle of rotation.
tan2theta = 6(dq.ft.6)/137 = 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!

PreCalculus 
bobpursley,
Using
Theta = 0.5 arccot((ac)/2/b)
Theta= 1/2 arccot((6/2)/6sqrt6
=1/2 arccot(1/2sqrt6)
I get slightly less than 40 deg 
PreCalculus 
Joanna Boyd,
Ellipse 34