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a line has intercepts a and b on the coordinate axis when the axes are rotated through an angle θ,keeping the origin fixed the line makes equal intercepts on the coordinate axes then tanθ=?

a line has intercepts a and b on the coordinate axis when the axes are rotated through an angle θ,keeping the origin fixed the line makes equal intercepts on the coordinate axes then tanθ=?

Grade:12

1 Answers

Vikas TU
14149 Points
9 years ago

 

When the axes are rotated through an angle θ,keeping the origin fixed then the graph looks like this:

 

 

 

Solving the eqns. x/a + y/b =1 with                                                            

we will get,

x = ab/(b + atanθ), y = abtanθ/(atanθ + b)

             AND

x = ab/(b - acotθ), y = abcotθ/(acotθ - b) as therir points. of intersections.

 

Now, it is said that the intercepts made by the line are equal.

Thus, ab/(b + atanθ) = abcotθ/(acotθ - b)

         solving this , it will reduce to

         

tanθ = (a-b)/(a+b)

is the answer.

 

 

 

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