parabola of a tangent

label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

For what values of a and b is the line

4x + y = b
tangent to the parabola
y = ax2
when x = 4?

Jul 15th, 2015

Thank you for the opportunity to help you with your question!

--------------------------------------------------------------------------------------------


Differentiating y w.r.t. x


This is the slope of tangent to the parabola at any point x.


At x = 4

Slope of the tangent is



Given that 

4x + y = b 

is a tangent to the parabola at x = 4


The equation of tangent can be rewritten as

y = -4x + b

Comparing the above equation with slope intercept form of a line

y = mx + b (where m is the slope of the line)

we get, slope of the tangent = -4


Therefore, 



So, equation of parabola becomes



At x = 4

y = 


(4, -8) is the point at which the tangent touches the parabola.

Substitute x = 4 and y = -8 in the equation of tangent to find b



ANSWER:  

--------------------------------------------------------------------------------------------

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 15th, 2015

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
Jul 15th, 2015
...
Jul 15th, 2015
Jun 25th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer