At what points on the hyperbola #xy=12# is the tangent line parallel to the line #3x+y=0#?

1 Answer
Noah G
Mar 8, 2018

The points are #(2, 6)# and #(-2, -6)#

Explanation:

We can see that #y =12/x#. The line #3x + y = 0# can be rewritten as #y = -3x#, which has a slope of #-3#. We want the tangent line parallel to have the same slop as the given line, thus, we want #y' = -3#.

#y' = -12/x^2#

So we need to have

#-3 = -12/x^2#

#x^2 = 4#

#x = +- 2#

#:.# The two points are #y(2) = 12/2 = 6# and #y(-2) = 12/(-2) = -6#.

Hopefully this helps!

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