Help with determining Angle of Rotation for a Conic, please.

[popsquare]

I am looking for the angle needed to rotate the conic to eliminate the xy-term
but the angle I find is negative and I need the counter-clockwise angle of rotation to satisfy 0 < theta < 90 degrees. Where am I going wrong? Or what else do I need to know? Thank you for your help.


I have this equation of a conic and I am supposed to find only the angle of rotation with this formula:

cot 2(theta) = A - C / B

The equation I am using is this:

153x^2 - 192 xy + 97y^2 - 30x -40y - 200 = 0​

I then solve for theta plugging these A = 153 , B = -192 , C = 97 into
cot 2(theta) = A - C / B

I get this equation: cot 2(theta) = -56/192

Let theta = 2*theta

Then :
cot theta = -56/192

I take the inverse tangent to find 2*theta and then solve for theta like this:
arctan ( 192/-56) = -73.7398 degrees

Remember I let theta = 2*theta

-73.7398 = 2*theta

theta = -37 degrees.

Is there a way for -37 degrees to satisfy the original question?

 

[HallsofIvy]

If one axis of the ellipse is at -37 degrees then the other axis, at right angles to that, is 90- 37= 53 degrees.

 

[popsquare]

i get it, thank you very much.