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  • Mixed term xy is to be removed from the general equation of second degree <img alt="\mathrm{a x^2+b y^2+2 h x y+2 g x+2 f y+c=0,}" src="https://entrancecorner.oncodecogs.com/gif.late

Mixed term xy is to be removed from the general equation of second degree

\mathrm{a x^2+b y^2+2 h x y+2 g x+2 f y+c=0,}

one should rotate the axes through an angle 

\mathrm{\theta} given by  \mathrm{ tan \: 2\theta}  equal to

 

Option: 1

\mathrm{\frac{(a-b)}{2h}}


Option: 2

\mathrm{\frac{2h}{a+b}}


Option: 3

\mathrm{\frac{a+b}{2h}}


Option: 4

\mathrm{\frac{2h}{(a-b)}}


Answers (1)

best_answer

Let \mathrm{\left(x^{\prime}, y^{\prime}\right)}, be the coordinates on new axes, then, put

\mathrm{x=x^{\prime} \cos \theta-y^{\prime} \sin \theta}

\mathrm{y=x^{\prime} \sin \theta+y^{\prime \prime} \cos \theta}

Then coefficient of \mathrm{x^{\prime} y^{\prime}} in transformed equation = 0, so,

\mathrm{2(b-a) \sin \theta \cos \theta+2 h \cos 2 \theta=0}

Or \mathrm{\tan 2 \theta=2 h /(a-b),} which is given in (d).

 

 

Posted by

Irshad Anwar

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