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Straight Lines and Pair of Straight Lines question

2003 · Shift 0 · Q109
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  5. /2003 · Shift 0 · Q109

Straight Lines and Pair of Straight Lines question

2003 · Shift 0 · Q109

JEE MainMathematicsStraight Lines and Pair of Straight LinesMCQ+4 / −1
A square of side a lies above the xxx-axis and has one vertex at the origin. The side passing through the origin makes an angle α(0<α<π4)\alpha \left( {0 \lt \alpha \lt {\pi \over 4}} \right)α(0<α<4π​) with the positive direction of x-axis. The equation of its diagonal not passing through the origin is :
  1. A
    y(cos⁡α+sin⁡α)+x(cos⁡α−sin⁡α)=ay\left( {\cos \alpha + \sin \alpha } \right) + x\left( {\cos \alpha - \sin \alpha } \right) = ay(cosα+sinα)+x(cosα−sinα)=a
  2. B
    y(cos⁡α−sin⁡α)−x(sin⁡α−cos⁡α)=ay\left( {\cos \alpha - \sin \alpha } \right) - x\left( {\sin \alpha - \cos \alpha } \right) = ay(cosα−sinα)−x(sinα−cosα)=a
  3. C
    y(cos⁡α+sin⁡α)+x(sin⁡α−cos⁡α)=ay\left( {\cos \alpha + \sin \alpha } \right) + x\left( {\sin \alpha - \cos \alpha } \right) = ay(cosα+sinα)+x(sinα−cosα)=a
  4. D
    y(cos⁡α+sin⁡α)+x(sin⁡α+cos⁡α)=ay\left( {\cos \alpha + \sin \alpha } \right) + x\left( {\sin \alpha + \cos \alpha } \right) = ay(cosα+sinα)+x(sinα+cosα)=a
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