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A square of side a lies above the x-axis...

A square of side a lies above the x-axis and has one vertex at the origin. The side passing through the origin makes and angle `alpha` (`0 lt alpha lt (pi)/(4)`) with the positive direction of x-axis. The equation of its diagonal not passing through the origin is

A

`y("cos"alpha+"sin"alpha) +x("sin"alpha-"cos" alpha) =a`

B

`y("cos"alpha+"sin"alpha) +x("sin"alpha+"cos" alpha) =a`

C

`y("cos"alpha+"sin"alpha) +x("cos"alpha-"sin" alpha) =a`

D

`y("cos"alpha-"sin"alpha) -x("sin"alpha-"cos" alpha) =a`

Text Solution

Verified by Experts

The correct Answer is:
C
The coordinates of A and B are as shown in the figure.

The equation of the diagonal AB is
`y-a " sin" alpha = (a "cos" alpha-a"sin"alpha)/(-a"sin"alpha-a"cos"alpha)(x-a"cos"alpha)`
`"or " y("cos" alpha+"sin"alpha)-a("sin"alpha " cos"alpha+"sin"^(2)alpha)`
`=-("cos" alpha-"sin"alpha)x+a"cos" alpha(" cos"alpha-"sin"alpha)`
`y("cos" alpha+"sin"alpha)+x("cos"alpha-"sin"alpha)=a`
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