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

Question

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

TestHub · Accepted Answer

Co-ordinates of A = ( a cos α , a sin α ) Equation of OB , y = tan ( 4 π ​ + α ) x CA ⊥ r to OB ∴ slope of CA = − cot ( 4 π ​ + 2 ) Equation of CA y − a sin α = − cot ( 4 π ​ + 2 ) ( x − a cos α ) y ( sin α + cos α ) + x ( cos α − sin α ) = a

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