Hello, ramiee2010!

You should be familiar with all the Rotation Formulas

. . before attempting this type of problem.

Given: ..[1]

Rotate the coordinate axes to remove the -term

Identify the type of the conic.

. . The angle of rotation is given by: . .[2]

. . The new coordinates are given by: . .[3]

We have: .

Then: .

is in a right triangle with: .

. . Pythagorus says: .

Hence: .

Identity: .

We have: .

Hence, is in a 3-4-5 right triangle: .

Substitute into [3]: .

Substitute into [1]:

. .

. . .

. .

. . . . . . .

. . . . . . . . . . .