Q6 of 59 Page 178

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.

Given: …(i)

and …(ii)


Firstly, we find the slope of the given lines






Since, the above equation is in y = mx + b form.


So, Slope of the eq. (i) is


Now, finding the slope of the eq. (ii)







Since, the above equation is in y = mx + b form.


So, Slope of the eq. (ii) is


Let θ be the angle between the given two lines.



Putting the values of m1 and m2 in above eq., we get







Hence, the required angle is


Hence Proved


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