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 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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