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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

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

Grade:11

2 Answers

akash kashyp
8 Points
12 years ago
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)
Badiuddin askIITians.ismu Expert
148 Points
12 years ago

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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