Q.

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 αa<α<π/4 with the positive direction of the x-axis. The equation of its diagonal not passing through the origin is

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a

ycosα+sinα+xsinα−cosα=a

b

ycosα+sinα+xsinα+cosα=a

c

ycosα+sinα+xcosα−sinα=a

d

ycosα−sinα−xsinα−cosα=a

answer is C.

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Detailed Solution

The coordinates of A and B are as shown in the figure.  The equation of the diagonal AB is y−asinα=acosα−asinα−asinα−acosαx−acosαor ycosα+sinα−asinαcosα+sin2α=−cosα−sinαx+acosαcosα−sinαor ycosα+sinα+xcosα−sinα=α
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