Y=(x^2) +1 and y = - (x^2)? tangent

  • Thread starter swechan02
  • Start date
  • #1
5
0
Find the equations of the lines that are tangent to both curves simultaneously:y=(x^2) +1 and y = - (x^2)? :eek:
 

Answers and Replies

  • #2
793
4
Find the equations for the tangent lines to both curves and set them equal to each other. You will find when the slope of the tangents are equal and then can make an equation(s) of of it.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
966
Jameson is correct but it's a bit more complicated than he implies.

Suppose a line is tangent to y= x2+ 1 at (x0,x02+ 1) and tangent to y= -x2 at (x1,-x12).
Any (non-vertical) line can be written as y= mx+ b. m is equal to the derivative of the functions at the given points: m= 2x0= -2x1 so x1= -x0. We must have x02+1= (2x0)x0+ 1 or b= 1- x02. We must also have -x12= (-2x1)x1+ b or b= x12. That is, b= x12= 1- x02. But since x1= -x0, x12= x02 so 1- x02= x02.

Solve that for x0 and then you can find m and b.

Because of the squares, there are, of course, two symmetric solutions,.
 
Last edited by a moderator:

Related Threads on Y=(x^2) +1 and y = - (x^2)? tangent

  • Last Post
Replies
7
Views
3K
Z
  • Last Post
Replies
12
Views
3K
  • Last Post
Replies
10
Views
71K
Replies
2
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
2K
Replies
3
Views
3K
Replies
3
Views
3K
Replies
1
Views
2K
Top