At what point on the paraboloid y = x2 + z2 is the tangent plane parallel to the plane 3x + 2y + 7z = 2? (if an answer does not exist, enter dne.) (x, y, z) =

If represent a family of surfaces for different values of the constant . The gradient of the function defined as is a vector normal to the surface .

Given the paraboloid

.

We can rewrite it as a scalar value function f as follows:



The normal to the paraboloid at any point is given by:



Also, the normal to the given plane is given by:



Equating the two normal vectors, we have:



Since, -1 = 2 is not possible, therefore there exist no such point on the paraboloid such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2.

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.