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.
Given a general conic:
If (that means it has a cross term).
Then the required angle is:
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You problem is,
The required angle satisfies,
Thus,
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When we rotate by we get the new coordinates:
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In this case thus,
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Substitute the new x and y coordinates:
Expand,
Combine,