Is a conic section with two branches and is cut when a plane cuts the double napped cone vertically *?

Answer:

1. Circle

2. Ellipse

3. Parabola

4. Hyperbola

FURTHER EXPLANATION

A cone is a shape that can be created when a plane intersects a double-napped cone. In other words, a conic section is a section of a double-napped cone. Depending on the angle of the plane to the cone, the cone can be a circle, ellipse, parabolic, or hyperbolic.

For a better understanding, see Fig 1.

1. If you will cut the double-napped cone using a plane figure horizontally, which of the following types of conic sections will be formed?

Circle  

A circle is a set of all points equidistant from a fixed point on the plane. A circle is formed if the cut plane is parallel to the base of the right cone (See Fig .1(a))

The general form of the equation for a circle centered at (a, b) and radius r (See Fig.2).

2. When the (tilted) plane intersects only one cone to form a bounded curve, which of the following types of conic sections will be formed?

Ellipse

An ellipse is the set of all points in the plane whose sum of distances from two fixed points in the plane is constant. If the plane intersects completely across the ceiling of the cone at an angle between and, the cone-plane intersection curve is an ellipse.

The standard equation for an ellipse centered at (a,b) with horizontal radius h and vertical radius k

3. When the plane intersects only one cone to form an unbounded curve, which of the following types of conic sections will be formed?

Parabolic

A parabola is a set of points in a plane that are equidistant from both the directrix (the fixed straight line) and the focus (the fixed point). A parabola occurs when the section plane is parallel to the surface of the cone and passes through the cone only.

The standard equation for a parabola (axis of symmetry parallel to the y-axis) with vertex at (a, b), focus at (a, b + p), and directrix y = b -p is:

Where p is the distance from the vertex to the focus.

4. When the plane (not necessarily vertical) intersects both cones to form two un-bounded curves, which of the following types of conic sections will be formed?

Hyperbola

A curve of intersection is a hyperbola if the plane of intersection is at an angle to the base that passes through both cones. A hyperbola is the set of all points in the plane that have a constant distance difference from two fixed points in the plane.

Hyperbolic standard equation centered at (a,b) with horizontal radius h and vertical radius k

Learn more about conic sections here:

brainly.ph/question/29206515?

#SPJ2