(A) The given equation is $x^2+4xy-y^2=0$. Comparing this with the general second-degree equation $Ax^2+Bxy+Cy^2=0$,we get $A=1, B=4, C=-1$. To elimin

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(A) The given equation is $x^2+4xy-y^2=0$. Comparing this with the general second-degree equation $Ax^2+Bxy+Cy^2=0$,we get $A=1, B=4, C=-1$. To eliminate the $xy$ term,the axes must be rotated by an angle $\theta$ such that $\cot(2\theta) = \frac{A-C}{B}$. Substituting the values,we get $\cot(2\theta) = \frac{1-(-1)}{4} = \frac{2}{4} = \frac{1}{2}$. Therefore,$\tan(2\theta) = 2$,which implies $2\theta = \tan^{-1}(2)$. Thus,$\theta = \frac{1}{2} \tan^{-1}(2)$.

Class 11 Mathematics Rectangular Cartesian Co-ordinates Transformation of axes

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The angle by which axes are to be rotated without changing the origin so that the transformed equation of $x^2+4xy-y^2=0$ in new coordinates $(X, Y)$ does not contain the $XY$ term is

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A
$\frac{1}{2} \tan^{-1}(2)$
B
$\tan^{-1}(2)$
C
$\frac{\pi}{8}$
D
$\frac{\pi}{4}$

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Rectangular Cartesian Co-ordinates

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Transformation of axes

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MediumAP EAMCET 2018

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MediumTS EAMCET 2024

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The angle by which axes are to be rotated without changing the origin so that the transformed equation of $x^2+4xy-y^2=0$ in new coordinates $(X, Y)$ does not contain the $XY$ term is

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