1. Find an equation for the set of points whose distance from the plane z =8 is twice the distance to the point (0,1,2). Identify this surface. You do not have to sketch this surface.

Identify the type of quadric surface defined by the equation and find all x-, y-, and z-intercepts of the resulting graph. Sketch the graph of this quadric surface on paper. The quadric surface is a / an hyperboloid of one sheet 1 x-intercepts when x = 3 1 2 y-intercepts when y = z-intercepts when z = -1 and 4y² - 9x² + z² = 1, ✓ with Enter your answers as comma separated lists, or enter NONE if there are no intercepts of a particular type.

Consider the following equation of a quadric surface. y² = z² X 100 25 + a. Find the intercepts with the three coordinate axes, if they exist. b. Find the equations of the xy-, xz-, and yz-traces, if they exist. c. Identify and sketch a graph of the surface. A. The surface intersects the x-axis at x = 0. (Use a comma to separate answers as needed.) B. There are no x-intercepts. Find the y-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice. A. The surface intersects the y-axis at y = 0. (Use a comma to separate answers as needed.) B. There are no y-intercepts. Find the z-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice. A. The surface intersects the z-axis at z = 0 . (Use a comma to separate answers as needed.) B. There are no z-intercepts. b. Find the equation of the xy-trace, if it exists. Select the correct choice and fill in any answer boxes within your choice. The trace is not a…