After a rotation of axes is used to eliminate the $x y$ -term from an equation of the form $A x ^ { 2 } + B x y + C y ^ { 2 } + D x + B y + F = 0$ the coefficients of the $x ^ { 2 }$ -and $y ^ { 2 }$ -terms remain $A$ and $C$ , respectively.

Question

After a rotation of axes is used to eliminate the

x y

-term from an equation of the form

A x ^ { 2 } + B x y + C y ^ { 2 } + D x + B y + F = 0

the coefficients of the

x ^ { 2 }

-and

y ^ { 2 }

-terms remain

A

and

C

, respectively.

Quizplus · Accepted Answer

The coefficients of the new equation, after rotation of axes, are obtained by making the substitutions. $\begin{array} { l } 
x = x ^ { \prime } \cos \theta - y ^ { \prime } \sin \theta \
y = x ^ { \prime } \sin \theta - y ^ { \prime } \cos \theta
\end{array}$

After a Rotation of Axes Is Used to Eliminate The x