We first recognise that parallel means that the slopes must be equal. Rearranging the equation, we get:
So that means we are looking for points along the curve with slope equal to
. To get those points, we need the derivative of the curve:
Using the quotient rule, we get:
So that means:
We are interested in points where the derivative is
This means we have to tackle two potential
values. At
, we have:
At
, we have:
So that means the tangent lines are are looking for are: for
.
and for