Tangent Lines, Parallel Lines, and Normal Lines

**kinana18** · January 25th 2009, 07:33 PM

Find an equation of each line normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0

**mollymcf2009** · January 25th 2009, 07:55 PM

Pretty sure it would just be y = 2x

It runs parallel to y=2x + 1 and would be perpendicular to the tangent lines at those points.

Are you supposed to find one line that will apply to both graphs?

**mr fantastic** · January 25th 2009, 08:41 PM

Originally Posted by kinana18

Find an equation of each line normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0

$y = \frac{2x}{x - 1} = 2 + \frac{2}{x-1} \Rightarrow \frac{dy}{dx} = \frac{-2}{(x-1)^2}$ .

You want the normal to be parallel to $2x - y + 1 = 0 \Rightarrow y = 2x + 1$ .

To find the x-coordinates of the required normal solve $\frac{(x-1)^2}{2} = 2$ : x = 0, 2.

Therefore the required normal is normal to the curve at (0, 0) and (2, 4). The equation of this normal is y = 2x.

Note: The normal is also the line of symmetry of the curve.

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