Substitute these new expressions for x and y into the given

Substitute these new expressions for x and y into the given equation, xy + 4 = 0. Then, simplify. (X - Y/Squareroot 2)(X + Y/Squareroot 2) + 4 = 0 (X + Y/Squareroot 2)(X + Y/Squareroot 2) = -4 (X - Y)(X + Y)/Squareroot 2 Squareroot 2 = -4 X^2 - Y^2/2 = -4 X^2 - Y^2 = 2 (-4) X^2 - Y^2 = X^2/- Y^2/= 1 Y^2/- X^2/= 1 Thus, using a rotation of axes to eliminate the xy-term gives us the following result. (Write an equation in XY-coordinates. Use a rotation angle that satisfies 0 lessthanorequalto lessthanorequalto pi/2.)

Solution

We have x²-y²=2(-4)

x²-y²=-8

Dividing both sides by -8

x²/-8 - y²/-8=1

y²/8 - x²/8 = 1