If a right circular cone is intersected by a plane that passes through only one nappe of the cone but is not parallel to an edge of the cone, as the picture below, what shape is produced?

C. An ellipse

Step-by-step explanation:

If you cut a cone on the side with an angle that will produce an ellipse-shaped plane.

if you were to cut the cone perpendicularly to its height (as if the double cone on the picture was straight up), you would get a circle as the plane, because it would be a transversal cut of a circular cone.

If you cut it with an angle, you're stretching the circle... so you'll have an ellipse.

It is NOT a parabola NOR a hyperbola, since both would require the cross-section to go through the base... which it does not in this problem.  Please refer to the image below.

(3,0) and (0,6)

Step-by-step explanation:

(x,y) is the only way to make ordered pair.

The x was a 3 so you could cross out the first and last because they put the 3 in the y spot. When is should be (3,0).

Then the y was 6 and that I would be (0,6) so the third would also be crossed out because they put the 6 in the y spot.

So the answer is (3,0) and (0,6).