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Area of a triangle formed by any tangent at any point and asymptotes of the hyperbola xy=2 .



04-Dec-2016 12:10 PM
~2

Answers (1)


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any point on a rectangular hyperbola xy=c2 is P(ct,c/t)..and slope at p is given by -1/t2 . write the equation of line(which is tangent to the given hyperbola) with slope -1/t2 and passing throught P...

then write the above equation of line in the  form of x/a + y/b =1...   you'll get a=2ct and b=2c/t.   now the are of triangle is ab/2 which is 2c2..  given c2=2 so are of triangle is 4

 

NOTE: The asymptotes of rectangular hyperbola xy=c2 are the coordinate axes.



11-02-2017 15:59
~8

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