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R Gopalakrishnan Grade: 11
        

Sir,


 I have a doubt in this question.


Show that the tangent of an angle between the lines x/a+ y/b=1 and x/a- y/b=1 is 2ab/a^2-b^2


Waiting for your reply

7 years ago

Answers : (2)

akash kashyp
8 Points
										dear gopalakrishnan


here tangent of angle means nothing but tanA(angle between the lines)

tanA=m1-m2/(1+m1*m2) where m1= -b/a m2= b/a (m1,m2 are slopes of given lines)
7 years ago
Badiuddin askIITians.ismu Expert
147 Points
										

Dear R Gopalakrishna


x/a+ y/b=1


slope of line m1=-b/a


x/a- y/b=1


slope of line m2=b/a


when two linw cut each other then two angel forms


tanθ=|(m1-m2)/(1+m1m2)|


        =|(-b/a-b/a)/(1-b2/a2)|


         =|2ab/(a2-b2)|


and other angel is 180-θ


tan(180-θ)=-tanθ=-|2ab/(a2-b2)|


we can combine both result   =2ab/(a2-b2)





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Badiuddin


7 years ago
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