To remove the xy term from the second-degree | vedclass

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(B) The general second-degree equation is given by $Ax^2 + 2hxy + By^2 + 2gx + 2fy + c = 0$.Comparing this with the given equation $5x^2 + 8xy + 5y^2

Vedclass · Accepted Answer

$\pi/4$

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(B) The general second-degree equation is given by $Ax^2 + 2hxy + By^2 + 2gx + 2fy + c = 0$.Comparing this with the given equation $5x^2 + 8xy + 5y^2 + 3x + 2y + 5 = 0$,we have $A = 5$,$h = 4$,and $B = 5$.To eliminate the $xy$ term,the axes must be rotated by an angle $	heta$ such that $	an(2	heta) = \frac{2h}{A - B}$.Substituting the values,we get $	an(2	heta) = \frac{2(4)}{5 - 5} = \frac{8}{0} = \infty$.Since $	an(2	heta) = \infty$,we have $2	heta = \frac{\pi}{2}$.Therefore,$	heta = \frac{\pi}{4}$.

To remove the $xy$ term from the second-degree equation $5x^2 + 8xy + 5y^2 + 3x + 2y + 5 = 0$,the coordinate axes are rotated through an angle $\theta$. Then $\theta$ equals:

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