x^2-10xy+y^2+1=0

I'm supposed to rotate the axes in order to eliminate the xy-term. I'm told this problem is very simple, but I don't understand this section at all. Any help is greatly appreciated.

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- Jun 4th 2007, 07:16 PMalreadyinuseRotation and Systems of Quadratic Equations
x^2-10xy+y^2+1=0

I'm supposed to rotate the axes in order to eliminate the xy-term. I'm told this problem is very simple, but I don't understand this section at all. Any help is greatly appreciated. - Jun 4th 2007, 07:37 PMThePerfectHacker
Given a general conic:

If (that means it has a cross term).

Then the required angle is:

---

You problem is,

The required angle satisfies,

Thus,

---

When we rotate by we get the new coordinates:

---

In this case thus,

---

Substitute the new x and y coordinates:

Expand,

Combine,

- Jun 4th 2007, 08:14 PMalreadyinuse
Thanks for helping me with the last problem. I know how to solve the rest of my homework except for this one:

xy-2y-4x=0

Am I supposed to change the equation first? - Jun 4th 2007, 08:16 PMThePerfectHacker
- Jun 4th 2007, 08:26 PMalreadyinuse
Ah, okay. *obviously braindead*

Thanks for all your help!