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  • A square of side a lies above the -axis and has one vertex at the origin. The side passing through the origin makes an angle

A square of side a lies above the x -axis and has one vertex at the origin. The side passing through the origin makes an angle \alpha\left(0<\alpha<\frac{\pi}{4}\right) with the positive direction of x -axis. The equation of its diagonal not passing through the origin is

Option: 1

y(\cos \alpha-\sin \alpha)-x(\sin \alpha-\cos \alpha)=a


Option: 2

y(\cos \alpha+\sin \alpha)-x(\sin \alpha-\cos \alpha)=a


Option: 3

y(\cos \alpha+\sin \alpha)+x(\sin \alpha+\cos \alpha)=a


Option: 4

y(\cos \alpha+\sin \alpha)+x(\sin \alpha-\cos \alpha)=a


Answers (1)

best_answer

Co-ordinates of  A=(a \cos \alpha, a \sin \alpha) ;

Equation of O B \quad y=\tan \left(\frac{\pi}{4}+\alpha\right) x

C A \perp \text { to } O B ; \quad \therefore \text { slope of } C A=-\cot \left(\frac{\pi}{4}+\alpha\right)

Equation \, \, of \, \, C A, y-a \sin \alpha=-\cot \left(\frac{\pi}{4}+\alpha\right)(x-a \cos \alpha)

\Rightarrow \quad y(\sin \alpha+\cos \alpha)+x(\cos a-\sin \alpha)=a

Posted by

shivangi.bhatnagar

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