# PreCalculus

posted by .

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

• PreCalculus -

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

• PreCalculus -

Ellipse -34

## Similar Questions

1. ### Geometry - Angle of rotation

What is the measure of the angle of rotation with respect to two lines that intersect to form a 25° angle?
2. ### geometry

What is the measure of the angle of rotation with respect to two lines that intersect to form a 45° angle?
3. ### Precalculus

Identify the graph of the equation. What is the angle of rotation for the equation?
4. ### Precalc

Identify the graph of the equation. What is the angle of rotation for the equation?
5. ### Math

[R] = [4/5 -3/5] and [S] = [-3/5 4/5] [-3/5 -4/5] and [4/5 3/5] are reflection matrices. Calculate [R·S] and verify that it can be identified as the matrix of rotation. Determine the angle of the rotation.
6. ### precalculus

use the discriminant to determine whether the equation is a parabola, an ellipse, or a hyperbola. Then identify the angle of rotation required to eliminate the xy-term. x^2+4xy+y^2=1 5x^2-6xy+5y^2-8x+8y-8=0 9x^2+24xy+16y^2=25
7. ### Math

Which of the following are necessary to describe a rotation of a figure on a coordinate plane ?
8. ### algebra

which of the following are necessary to describe a rotation of a figure on a coordinate plane?
9. ### Pre-cal

Describe the distance of point P from the far left or right of the center of the wheel as a function of the angle of the rotation. Assume that the wheel is rotating counterclockwise and the angle of rotation,theta, is the angle between …
10. ### math

Describe the distance of point P from the far left or right of the center of the wheel as a function of the angle of the rotation. Assume that the wheel is rotating counterclockwise and the angle of rotation,theta, is the angle between …

More Similar Questions