Substitute these new expressions for x and y into the given equation, xy + 4 = 0

Question

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.)

Explanation / Answer

We have x2-y2=2(-4)

x2-y2=-8

Dividing both sides by -8

x2/-8 - y2/-8=1

y2/8 - x2/8 = 1

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.