Analytical Geometry> Straight lines...

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

R Gopalakrishnan , 16 Years ago

Grade 11

2 Answers

akash kashyp

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)

Last Activity: 16 Years ago

Badiuddin askIITians.ismu Expert

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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Last Activity: 16 Years ago