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 < π/4 ) with - Mathematics MCQ AIEEE-CBSE-ENG-03 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

The vertices adjacent to the origin (0, 0) are (a cos α, a sin α) and (a cos (α + π /2), a sin (α + π /2)) = (- a sin α, a cos α) .The diagonal passes through (a cos α, a sin α) and (- a sin α, a cos α) .Slope m = \frac{a c o s α - a s i n α}{- a s i n α - a c o s α} = - \frac{c o s α - s i n α}{c o s α + s i n α} .Equation: y - a sin α = - \frac{c o s α - s i n α}{c o s α + s i n α} (x - a cos α) $ y (cos α + sin α) - a sin α cos α - a sin^{2} α = - x (cos α - sin α) + a cos^{2} α - a sin α cos α $ y (cos α + sin α) + x (cos α - sin α) = a (sin^{2} α + cos^{2} α) = a

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

y (cos α - sin α) - x (sin α - cos α) = a

y (cos α + sin α) + x (sin α - cos α) = a

y (cos α + sin α) + x (sin α + cos α) = a

y (cos α + sin α) + x (cos α - sin α) = a

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