Question

question 7 of 10 a(n) ______ is produced when you slice a cone with a plane that passes through only one nappe of the cone but is not parallel to an edge of the cone. a. circle b. hyperbola c. ellipse d. parabola

Explanation:

Answer:

C. ellipse

Wait, no—wait, let's recheck. Wait, the correct conic section when a plane slices one nappe not parallel to an edge (and not parallel to the axis for circle, or cutting both nappes for hyperbola, or parallel to edge for parabola). Wait, actually:

• Circle: plane perpendicular to axis, cutting one nappe.
• Ellipse: plane cutting one nappe, not perpendicular to axis, not parallel to edge.
• Parabola: plane parallel to an edge (generator) of the cone, cutting one nappe.
• Hyperbola: plane cutting both nappes.

So the question says "passes through only one nappe" and "not parallel to an edge". So that's ellipse? Wait, no, wait the original question's option D was marked, but maybe that's a mistake. Wait, let's re-express:

When a plane cuts one nappe of a cone, and is not parallel to a generator (edge), the intersection is an ellipse (if the plane is not perpendicular, but for circle it's perpendicular). Wait, no:

• If plane is perpendicular to axis: circle (one nappe, not parallel to edge).
• If plane is at an angle to axis, cutting one nappe, not parallel to generator: ellipse.
• If plane is parallel to generator: parabola (one nappe, parallel to edge).
• If plane cuts both nappes: hyperbola.

So the question says "passes through only one nappe" and "not parallel to an edge (generator)". So that should be ellipse? Wait, but the option D was marked as parabola, but parabola is when parallel to edge. So maybe the question's wording is "not parallel to an edge"—so if it's not parallel to edge, then it's ellipse (or circle). But circle is a special case of ellipse. Wait, maybe the correct answer is C. ellipse? Wait, no, let's check standard conic sections:

• Ellipse: plane intersects one nappe, angle of plane is between 0 (axis) and 90 degrees (perpendicular), not parallel to generator.
• Parabola: plane parallel to generator (angle equal to angle of generator with axis).
• Hyperbola: plane intersects both nappes (angle less than angle of generator, so cuts both).

So the question: "slice a cone with a plane that passes through only one nappe of the cone but is not parallel to an edge of the cone". So "not parallel to edge (generator)"—so plane is not parallel to generator, so intersection is ellipse (or circle). So the correct answer is C. ellipse. But the original marked option was D, which is wrong. So the correct answer is C. ellipse.

Wait, but maybe I made a mistake. Let's confirm:

• Circle: plane ⊥ to axis, one nappe, not parallel to edge (since edge is at an angle, plane is perpendicular, so not parallel).
• Ellipse: plane at angle to axis, one nappe, not parallel to edge (generator).
• Parabola: plane parallel to edge (generator), one nappe.
• Hyperbola: plane cuts both nappes.

So the question says "not parallel to an edge"—so parabola is parallel to edge, so excluded. So the answer is ellipse (C) or circle (A). But circle is a special case of ellipse. But the options have circle and ellipse. So if the plane is not perpendicular (so not circle) and not parallel to edge, then ellipse. So the correct answer is C. ellipse.

But the original marked option was D, which is incorrect. So the correct answer is C. ellipse.

So the final answer is C. ellipse.