The line #y=-3x+c# crosses the hyperbola #xy=12# twice. Find the range of possible values for c?

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Answer 1 · 2018-01-30T02:53:55

#c > 12# and #c < -12#

To find the x coordinate(s) of the intersection(s), start with:

#xy=12#

Substitute #y=-3x+c#:

#x(-3x+c)=12#

#-3x^2+cx-12=0#

For there to be two x coordinates of intersection, the discriminant of the above quadratic must be greater than 0:

#c^2-4(-3)(-12)>0#

#c^2>144#

#c > 12# and #c < -12#