8x^2 - 4xy + 5y^2 = 36
@=theta
1. Find tan 2@ and find cos 2@
2. Find sin@ and cos@
3. Transform the equation xy=1 by rotation, thus eliminating the xy term.
Hello, The Real Cosby!
You should be familiar with the "Rotation" formulas.
Otherwise, you should not have been assigned this problem.
The general quadratic equation is: .
We have: .
1. Find and
Formula: .
We have: .
Since is in Quadrant 2: .
is in a right triangle with:
Using Pythagorus, we get: .
Therefore: .
Since is in Quadrant 2, then is in Quadrant 1.2. Find and
Identities: .
We have: .
Formulas: .3. Transform the equation xy=1 by rotation, . ??
. . thus eliminating the xy term.
We have: .
Substitute into [1]: .
. .
. .
. .
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Drat! .I just figured out what #3 meant . . .
It is a separate problem!
We have: .
. . That is: .
. . It is a hyperbola rotated through 45°.
Hence: .
Substitute into [2]: .
. . Therefore: .
I need a nap . . .
.