Question

Consider the ellipse (x² / 4) + (y² / 1) = 1. What is the equation describing this ellipse after it has been rotated thirty degrees counterclockwise?

Answer 1

Any ideas????

Answer 2

$$
\dfrac {((x-h)\cos(A)+(y-k)\sin(A))^2}{(a^2)}+\dfrac{((x-h) \sin(A)-(y-k) \cos(A))^2}{(b^2)}=1
$$

Where <h,k> is the center of your ellipse: <h,k> = <0,0>, A is your angle of Rotation, \(30^{\circ}\), a=2 and y=1.

Source: http://math.stackexchange.com/questions/426150/what-is-the-general-equation-of-the-ellipse-that-is-not-in-the-origin-and-rotate

Answer 3

Nope-
The answer is 7x² - 6√(3)xy + 13y² - 16 = 0. For more information om the theory behind how it works, the amount of writing needed to arrive at the answer on a test, and a thorough discussion of the above example, see the linked sources.

Source(s):

http://en.wikipedia.org/wiki/Rotation_of...
http://www2.krellinst.org/UCES/archive/r...