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a line make intercept a and b on the coordinate axes.now axis is rotated by angle x.now that line make equal intercept on the new coordinate axis.what is the value of tanx

a line make intercept a and b on the coordinate axes.now axis is rotated by angle x.now that line make equal intercept on the new coordinate axis.what is the value of tanx

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Manoj

equation of line in first co ordinate system

x/a  +y/b =i

let new coordinaate system are x' and y'

so x' =xcosΘ +ysinΘ

   y' = ycosΘ -xsinΘ

so equation of line in new co ordinate system

x'/c +y'c =1

now put value of x' and y'

x(cosΘ -sinΘ)/c  + y( sinΘ + cosΘ)/c =1

these two line are same

so  (cosΘ -sinΘ)  =c/a

    ( sinΘ + cosΘ) =c/b

 solve these two

tan Θ =(a-b)/(a+b)

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