# For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 wh

• Feb 12th 2008, 12:06 PM
plstevens
For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 wh
__a=1/2
__b=-8
__a=-1/2
__b=8
__a=-20
• Feb 12th 2008, 02:02 PM
Jhevon
Quote:

Originally Posted by plstevens
__a=1/2
__b=-8
__a=-1/2
__b=8
__a=-20

what does wh in your question mean?

are the list of a's and b's you gave options to choose?
• Feb 12th 2008, 05:36 PM
plstevens
the wh, should be when x=4, and the a's and b's are th choices that i was given
• Feb 12th 2008, 06:51 PM
topsquark
Quote:

Originally Posted by plstevens
the wh, should be when x=4, and the a's and b's are th choices that i was given

Well, given the parabola $\displaystyle y = ax^2$, what is the equation of the line tangent to it at x = 4?

The tangent line must pass through the point (4, 16a).

$\displaystyle y^{\prime} = 2ax$, so when x = 4 the slope of the tangent line is $\displaystyle 2 \cdot a \cdot 4 = 8a$.

So the equation of the line that passes through the point (4, 16a) that has a slope of 8a is:
$\displaystyle y = mx + b$

$\displaystyle y = (8a)x + b$

Insert the point (4, 16a) to find b:
$\displaystyle 16a = (8a)(4) + b$

$\displaystyle b = 16a - 32a = -16a$

So the tangent line is $\displaystyle y = (8a)x - (16a)$ or in the form given in the problem:
$\displaystyle -(8a)x + y = -16a$

Compare this with
$\displaystyle 4x + y = b$

What are your values for a and b?

-Dan