Question is

Let f(x, y) = 100 + 10x + 25y – x^2 – 5y^2.

a. Describe the cross section of the surface Z = f(x, y) produced by cutting it with the planes Y = 0, y = 1, y = 2, and y = 3.

b. Describe the cross section of the surface in the planes x = 0, x = 1, x = 2, and x = 3.

c. Describe the surface z = f(x, y)

What I have done for part b:

Z = F(0,y) = 100 + 10x + 25y – x^2 – 5y^2

= 100 + 10(0) + 25y – (0)^2 – 5y^2

= 100 + 25y - 5y^2

z = F(1,y) = 100 + 10x + 25y – x^2 – 5y^2

= 100 + 10(1) + 25y – (1)^2 – 5y^2

= 111 + 25y - 5y^2

z = F(2,y) = 100 + 10x + 25y – x^2 – 5y^2

= 100 + 10(2) + 25y – (2)^2 – 5y^2

= 124 + 25y - 5y^2

z = F(3,y) = 100 + 10x + 25y – x^2 – 5y^2

= 100 + 10(3) + 25y – (3)^2 – 5y^2

= 139 + 25y - 5y^2

How i described the results:

The cross section of f(x, y) = 100 + 10x + 25y – x2 – 5y2 that correspond to x = 0, x = 1, x = 2, and x = 3 are upper semicircles with centres (0, 0, 0), (1, 0, 0), (2, 0, 0), (3, 0, 0) respectively.

Is this correct so far?