Question: (a) Part of a landscape generated in a computer game is defined by the quadric surface

\(z=3{{x}^{2}}+2xy+{{y}^{2}}+10x+2y+5\).

1. Obtain the critical point of the surface and determine if it is a maximum, a minimum or a saddle point.
2. Determine the equation of the tangent plane to the surface at the point where \(x=-1\) and \(y=0\).
3. Find or state a vector that is parallel to the normal to the surface where \(x=-1\) and \(y=0\).

(b) (i) Construct the bilinear surface patch based on the line segments joining \[A\left( 1,\,1,\,0 \right)\] with \[B\left( 2,\,1,\,1 \right)\] and \[C\left( 1,\,2,\,0 \right)\] with \[D\left( 2,\,2,\,0 \right)\] .

(ii) Obtain the parametric equations of the curve joining A to D .

(iii) Show that the curve joining B to C is a parabola lying in the plane \[x+y=3\] .

Price: $2.99

Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document