iran-konkur 2015 Q138

iran-konkur · Other · konkur-riazi_1394 Conic sections Conic Identification and Conceptual Properties
138- The rotation matrix $A$, with the relation $\begin{bmatrix} x \\ y \end{bmatrix} = A \cdot \begin{bmatrix} x' \\ y' \end{bmatrix}$, transforms the conic equation $5x^2 + 24xy - 2y^2 = 12$ into standard form with respect to $x'$ and $y'$. What is the tangent of the rotation angle?
(1) $\dfrac{2}{3}$ (2) $\dfrac{3}{4}$ (3) $\dfrac{4}{3}$ (4) $\dfrac{3}{2}$
\textbf{138-} The rotation matrix $A$, with the relation $\begin{bmatrix} x \\ y \end{bmatrix} = A \cdot \begin{bmatrix} x' \\ y' \end{bmatrix}$, transforms the conic equation $5x^2 + 24xy - 2y^2 = 12$ into standard form with respect to $x'$ and $y'$. What is the tangent of the rotation angle?

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(1) $\dfrac{2}{3}$ \hfill (2) $\dfrac{3}{4}$ \hfill (3) $\dfrac{4}{3}$ \hfill (4) $\dfrac{3}{2}$

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