The mixed term xy is to be removed from the g | vedclass

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(D) Let $(x', y')$ be the coordinates on the new axes. The transformation equations are $x = x' \cos 	heta - y' \sin 	heta$ and $y = x' \sin 	heta

Vedclass · Accepted Answer

$\frac{2h}{a - b}$

Vedclass · Answer

(D) Let $(x', y')$ be the coordinates on the new axes. The transformation equations are $x = x' \cos 	heta - y' \sin 	heta$ and $y = x' \sin 	heta + y' \cos 	heta$.Substituting these into the general equation $ax^2 + by^2 + 2hxy + 2fy + 2gx + c = 0$,the coefficient of the $x'y'$ term must be zero for the mixed term to be removed.The coefficient of $x'y'$ is given by $2(b - a) \sin 	heta \cos 	heta + 2h(\cos^2 	heta - \sin^2 	heta) = 0$.This simplifies to $-(a - b) \sin 2	heta + 2h \cos 2	heta = 0$.Rearranging gives $2h \cos 2	heta = (a - b) \sin 2	heta$.Therefore,$	an 2	heta = \frac{2h}{a - b}$.

The mixed term $xy$ is to be removed from the general equation $ax^2 + by^2 + 2hxy + 2fy + 2gx + c = 0$. One should rotate the axes through an angle $\theta$ given by $\tan 2\theta$ equal to:

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