You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
Tangent points to 2 surfaces: x^2-xy+z=0 and (x-1)^2+(y+1)^2+z=10
- Thread starter tparker73
- Start date
Please show your work so we may help you where you have gone wrong [if you have]. You should also readProblem is: find points where surfaces x^2-xy+z=0 and (x-1)^2+(y+1)^2+z=10 are tangent.
I get as far as finding the gradients of each but can't figure out where to go from there. Anyone have an idea?
Thanks.
http://www.freemathhelp.com/forum/threads/77972-Read-Before-Posting!!
Problem is: find points where surfaces x^2-xy+z=0 and (x-1)^2+(y+1)^2+z=10 are tangent.
I get as far as finding the gradients of each but can't figure out where to go from there. Anyone have an idea?
Thanks.
F(x,y,z)= x^2-xy+z
G(x,y,z)= (x-1)^2+(y+1)^2+z
Gradient of F = <2x-y, -x, 1>
Gradient of G = <2(x-1), 2(y+1), 1>
I need to find the point or points where these two level surfaces are tangent. I feel like I need to do a cross product of these somewhere but I am lost as to what the next step is.
Last edited:
D
Deleted member 4993
Guest
.F(x,y)= x^2-xy+z ← LHS says F is function of two variables. However RHS has three variables.
G(x,y)= (x-1)^2+(y+1)^2+z← LHS says G is function of two variables. However RHS has three variables.
Check your definitions carefully.
Gradient of F = <2x-y, -x, 1>
Gradient of G = <2(x-1), 2(y+1), 1>
I need to find the point or points where these two level surfaces are tangent. I feel like I need to do a cross product of these somewhere but I am lost as to what the next step is.
What is the relationship between the gradient of a function and the normal to the tangent plane?