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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 α (0<α<π4) with the positive direction of x-axis. The equation of its diagonal not passing through the origin is

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a

y(cosα−sinα)−x(sinα−cosα)=a

b

y(cosα+sinα)−x(sinα−cosα)=a

c

y(cosα+sinα)+x(sinα+cosα)=a

d

y(cosα+sinα)+x(sinα−cosα)=a

answer is B.

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Detailed Solution

Slope of the diagonal=tan(3π4+α)=−1+tanα1+tanα=sinα−cosαsinα+cosαAny point on the diagonal is (acosα, asinα)The equation is y−asinαx−acosα=sinα−cosαsinα+cosα or y(sinα+cosα)−x(sinα−cosα)=a

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