Question

Use appropriate software to graph the surfaces
Z=7-(x^2+y^2)
and
z=1-2x+6y
on a
common screen using the domain
|x|≤10, |y|≤10
and observe the curve of intersection
of these surfaces. Show that the projection of this curve onto the xy–plane is a circle by
showing the calculation and the details of the circle equation.

Answer 1

Intersection of these surfaces:

$$z = 7-x^2-y^2=1-2x+6y$$ $$7+9= x^2-2x +1+y^2+6y+9$$ $$(x-1)^2+(y+3)^2=4^2$$

Therefore, it is circle with radius 4, and center in point x=1, y=-3.