- #1
Pavoo
- 17
- 0
Homework Statement
Consider a surface ω with equation:
[tex]x^2 + y^2 + 4z^2 = 16[/tex]
Find an equation for the tangent plane to ω at point (a,b,c).
Homework Equations
Tangent plane, 3 variables:
[tex]f_{1}(a,b,c)(x-a) + f_{2}(a,b,c)(y-b) + f_{3}(a,b,c)(z-c)= 0[/tex]
The Attempt at a Solution
I get at the end:
[tex]ax + by + 4cz = a^2 + b^2 + 4c^2[/tex]
The textbook gives me:
[tex]ax + by + 4cz = a^2 + b^2 + 4c^2 = 16[/tex]
Where does the 16 come from?
Comparing to this problem, as an example:
Find an equation of the tangent plane to the sphere [tex]x^2 + y^2 + z^2 = 6 [/tex] at point (1,-1,2). This on is simple. But not the first above.
And is it possible to solve this by expanding to a fourth variable, such as ω?