4. Given the equation x 2 + 2y 2 − 3z 2 = 1
a. What is the name of a surface of this type?
b. Graph the surface, include the graph with your submitted work.
c. What curves occur at the intersection of the surface with any plane parallel to the xy-plane?
d. What curves occur at the intersection of the surface with any plane parallel to the xz-plane?
e. Find z x and x y
5. Find the minimum value of the function (x, y, z) = x 2 + y 2 + z 2 subject to the constraint x + y + z = 1
Please answer and show all work for these problems.Given the equation x 2
+2y 2
−3z 2
=1 a. What is the name of a surface of this type? b. Graph the surface, include the graph with your submitted work. c. What curves occur at the intersection of the surface with any plane parallel to the xy-plane? d. What curves occur at the intersection of the surface with any plane parallel to the xz-plane? e. Find ∂x
∂z
​
and ∂y
∂x
​
5. Find the minimum value of the function f(x,y,z)=x 2
+y 2
+z 2
subject to the constraint x+y+z=1