Understanding cot2(theta) = A-C / B

1. Mar 28, 2016

Terrell

1. The problem statement, all variables and given/known data
How did it go from A'x'^2 + B'x'y' + C'y'^2 + D'x' +E'y' + F = 0 to become B' = 2(C-A)sin(theta)cos(theta) + B(cos^2(theta) - sin^2(theta))?

*this is not an assignment, im just self studying :P

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Last edited: Mar 28, 2016
2. Mar 28, 2016

blue_leaf77

Expand the top most equation then collect the terms based on the powers of $x'$ and $y'$. To obtain (12), just keep track on the terms in the top most equation which contain $x'y'$.

3. Mar 28, 2016

andrewkirk

The latter is not a deduction from the former. It is simply a definition, which the author is free to make, as the symbol B' has not been used up to that point.

The deduction is the equation immediately after the 'where...' part.

4. Mar 28, 2016

Terrell

yes. i got that part, but how do i get from the 2nd equation to the third equation?

5. Mar 28, 2016

Terrell

but how do i deduce it? what is step1? i don't know how to start.. from A'x'^2 + B'x'y' + ... + F = 0 to B' = 2(C - A)...

6. Mar 28, 2016

blue_leaf77

Like andrew has said, $B'$ is just a symbol used to represent the coefficient of $x'y'$. The author could have retained the original form of the coefficient in terms of $A$, $B$, $C$, and $\theta$, but it will require more space. He chose $B'$ as the new coefficient for $x'y'$ because this symbol has not been used in the previous derivation.

7. Mar 29, 2016

Terrell

i got it! just keep track and combine all the terms with x'y' then equate to zero and simplify. thanks guys!