Tangent Lines, Parallel Lines, and Normal Lines

• Jan 25th 2009, 08:33 PM
kinana18
Tangent Lines, Parallel Lines, and Normal Lines
Find an equation of each line normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0
• Jan 25th 2009, 08:55 PM
mollymcf2009
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?
• Jan 25th 2009, 09:41 PM
mr fantastic
Quote:

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.