question_answer

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 \[\left( 0<\alpha <\frac{\pi }{4} \right)\] with the positive direction of X-axis. The equation of its diagonal not passing through the origin is     AIEEE  Solved  Paper-2003

A) \[y(\cos \alpha -\sin \alpha )-x(\sin \alpha -\cos \alpha )=a\]

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

C) \[y(\cos \alpha +\sin \alpha )+x(\sin \alpha +\cos \alpha )=a\]

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

Correct Answer: D

Solution :

Line OA makes an angle a with x-axis and OA = a, then coordinates of A are .             Also, , then, OB makes an angle  with x-axis, then coordinates of B are                                 i.e.,                            Equation of the diagonal not passing through the origin is                                                   \[\therefore \,\,y(\sin \alpha \,+\cos \alpha )\,+x\,(\cos \alpha -\sin \,\alpha )=0\]