Rotation Of Axes

Step 1: Rotate the coordinate system. We are given the equation

3x%5E2%20%2B%202%5Csqrt%7B3%7Dxy%20%2B%20y%5E2%20%3D%200

and we need to remove the

xy

-term by rotating the coordinate system. The angle

%5Ctheta

of rotation is given by:

%5Ctan%202%5Ctheta%20%3D%20%5Cfrac%7B2B%7D%7BA%20-%20C%7D

where

A%20%3D%203

B%20%3D%20%5Csqrt%7B3%7D

, and

C%20%3D%201

. Substituting these values:

%5Ctan%202%5Ctheta%20%3D%20%5Cfrac%7B2%5Csqrt%7B3%7D%7D%7B2%7D%20%3D%20%5Csqrt%7B3%7D.

Thus,

%5Ctheta%20%3D%2045%5E%5Ccirc

. Step 2: Apply the transformation. Using the formulas for coordinate rotation, we find the transformed equation:

(2%20%2B%20%5Csqrt%7B3%7D)x%5E2%20%2B%20(2%20-%20%5Csqrt%7B3%7D)y%5E2%20%2B%202xy%20%3D%204.

Chapter Questions
1 MCQs