# tangent of a parabola

• Feb 23rd 2008, 02:05 AM
andrew2322
tangent of a parabola
hi all pls all

Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12

• Feb 23rd 2008, 04:29 AM
Plato
Quote:

Originally Posted by andrew2322
Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12

The slope at each point on the parabola is 2x-1.
Now why don't you show us what you have done on your own.
• Feb 23rd 2008, 08:31 AM
TheEmptySet
$\displaystyle \frac{dy}{dx}=2x-1$

Since the line is written in slop intercept form
$\displaystyle y=x+c$ we know that the slope of line is
$\displaystyle m=1$

Since we need the slope to equal the derivative we get...

$\displaystyle 1=2x-1$ solving for x we get

$\displaystyle x=1$ This gives us half of the ordered pair...

plugging this into the equation of the parabola we get

$\displaystyle y=(1)^2-(1)-12=-12$ This completes our ordered pair giving us (1,-12)

Now finally we use this ordered pair to solve for c plugging the ordered pair into the equation of the line we get....
$\displaystyle -12=1+C$ solving for C we finally end up with...

$\displaystyle y=x-13$

I hope this helps. Remember that the derivative represents the slope of the graph at any point.(Rock)