Which refers to a set of points that are at a constant distance from a fixed point called vertex?
A parabola can be described as the set of coplanar points each of which is the same distance from a fixed focus as it is from a fixed straight line called the directrix. The midpoint between the focus and the directrix is the vertex. The line passing through the focus and the vertex is the axis of the parabola.
A conic section is a locus of a point P which moves in such a way that its distance from a fixed point S always bears a constant ratio to its distance from a fixed line, all being in the same plane. The fixed point is called focus and the fixed line is called directrix.
Definition. A parabola is the set of all points whose distance from a fixed point, called the focus, is equal to the distance from a fixed line, called the directrix. The point halfway between the focus and the directrix is called the vertex of the parabola.
The locus of a point which moves in a plane such that the ratio of its distance from a fixed point to its perpendicular distance from a fixed straight line is always constant, is called a conic. The constant ratio is called the eccentricity of the conic It is denoted by e.
Parabola. A parabola is "the set of all points in a plane equidistant from a fixed point (focus) and a fixed line (directrix)". The distances to any point (x,y) on the parabola from the focus (0,p) and the directrix y=-p, are equal to each other.
Ellipse. The set of all points such that the sum of the distances from the point to each of two fixed points is constant.
The fixed vertical line here is called the Axis. The line which is rotating is called the Generator. The fixed angle is called Vertex Angle. The intersection point of two lines is called Vertex.
The fixed point in a circle which is at a fixed distance from any point on the circumference is known as the center of the circle.
2. When a straight line intersect a vertical line at the fixed point and rotate about the fixed point. The surface obtained is called a double right circular cone.
The Hyperbola
A hyperbola is the set of points in the plane, the difference of whose distances from two fixed points, called the foci, remains constant.
Which of the following is a type of conic section that is a set of all coplanar points such that the sum of its distances from two fixed point is constant?
Key Concepts. An ellipse is the set of all points (x,y) in a plane such that the sum of their distances from two fixed points is a constant.
The vertical line is called the line of symmetry and divides the parabola into two halves that are mirror images. (If you folded the graph along the line of symmetry, the two halves would coincide exactly.)
Parabola: the set of points in a plane that are equidistant from a given point (focus F) and a given line (directrix). Standard equation: y = a(x – h) 2 + k. If a > 0, the parabola opens up. If a < 0, the parabola opens down.
An ellipse is the locus of all those points in a plane such that the sum of their distances from two fixed points in the plane, is constant. The fixed points are known as the foci (singular focus), which are surrounded by the curve. The fixed line is directrix and the constant ratio is eccentricity of ellipse.
Ellipse: The angle between the plane and the axis is greater than the vertex angle. This is shown in the upper nappe of 2 below. (Notice that a circle is a special type of ellipse.)
A set of points equidistant from a fixed point in a plane figure is called a circle where the distance between each of the set of the points and the fixed point forms the radius of the circle.
Parabola - A parabola is the set of all points (h, k) that are equidistant from a fixed line called the directrix and a fixed point called the focus (not on the line.) 2.) Axis of symmetry - A line passing through the focus and being perpendicular to the directrix.
The correct option is A circle. A circle is a set of points that are equidistant from a fixed point on a given surface.
Definition: An ellipse is the set of all points the sum of whose distances from two distinct fixed points (foci) is a constant.
A circle is the set of all points in a plane that are a fixed distance from a given point. The center of the circle is the point equidistant from all points on the circle. A radius of a circle is a line segment with one endpoint being the center of the circle, the other endpoint being a point on the circle.
Which of the following is the set of points such that the sum of the distances from any point on the ellipse to two other fixed points is constant?
An ellipse is a set of points in a plane such that sum of the distances from each point to two set points called the foci is constant. If you fixed two points in a plane and tied a string to each of these points leaving slack in the string and pulled it taut tracing in a loop, you would form an ellipse.
conic section, also called conic, in geometry, any curve produced by the intersection of a plane and a right circular cone. Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola.
Ellipse: When the plane intersects the double napped cone such that the angle between the vertex and the angle is greater than the vertex angle, the resulting conic section in the form of a closed curve is called an ellipse.
A parabola is defined as the conic section formed when a plane parallel (having the same slope) to the generator line intersects one nappe of a cone. In the figure below, you can see that the plane is parallel to the cone's generator line. The graph shows the intersection of the cone and plane.
The fixed distance is called the radius of the circle. A line segment with each of its endpoints on the circle, that passes through the center of the circle, is called a diameter of the circle. The length of a diameter is twice the radius.
Radius is a line segment joining the center of the circle and at any point on the boundary of circle..
Fixed points are also called critical points or equilibrium points.
By changing the angle and the location of the intersection, a parabola, circle, ellipse or hyperbola is produced. How are these sections created? When a plane intersects a double-napped cone and is parallel to the base of a cone, a circle is formed.
If the plane intersects one of the pieces of the cone and its axis but is not perpendicular to the axis, the intersection will be an ellipse.
A circle is the set of points in a plane that are all the same distance from a fixed point in the plane. The fixed point is called the centre of the circle.
What do you call the straight line that is rotated about a fixed point from a vertical line to form the double right circular cone?
A double right circular cone consist of two cones joined at the fixed point called the vertex. A line that rotates about the vertex is called the generator. The line that remain fixed is called the axis. The right circular cone has a circular base and its axis is always perpendicular to its base.
A conic section is a curve obtained by the intersection of a plane with the surface of a (double-napped) cone, as shown in Figure 4. When the plane is parallel to the edge of one cone , the intersection is a parabola.
An ellipse can be defined as the shape created when a plane intersects a cone at an angle to the cone's axis. It is one of the four conic sections. (the others are an circle, parabola and hyperbola).
Definition of Line of Symmetry
A line of symmetry is the line that divides a shape or an object into two equal and symmetrical parts. We also call this line the axis of symmetry or mirror line because it divides the figure symmetrically, and the divided parts look like mirror reflections of each other.
By completing the square, we have y=(x−4)2−6=(4−x)2−6. From this, we can see the y coordinates of two points equidistant from x=4 must be the same and the quadratic graph is symmetrical about the line x=4.
A set of points equidistant from a fixed point in a plane figure is called a circle where the distance between each of the set of the points and the fixed point forms the radius of the circle.
A parabola can be described as the set of coplanar points each of which is the same distance from a fixed focus as it is from a fixed straight line called the directrix. The midpoint between the focus and the directrix is the vertex.
Parabola - A parabola is the set of all points (h, k) that are equidistant from a fixed line called the directrix and a fixed point called the focus (not on the line.) 2.) Axis of symmetry - A line passing through the focus and being perpendicular to the directrix.
Definition: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.
If the cutting plane is parallel to two generators, this intersects nappes of the cone, and a hyperbola is obtained.
What type of curve is created by the intersection of a plane cutting parallel to one of the generators of cone?
If the cutting plane is parallel to exactly one generating line of the cone, then the conic is unbounded and is called a parabola. In the remaining case, the figure is a hyperbola: the plane intersects both halves of the cone, producing two separate unbounded curves.
Definition: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. We use the symbol ⊙ to represent a circle.
The distance from the centre of a circle to any point on the boundary is called the radius.
Locus. The idea of "the set of all points that ..." is used so much it has a name: Locus. A Locus is a set of points that share a property. So, a circle is "the locus of points on a plane that are a fixed distance from the center".
A circle is the set of all points in a plane that are a fixed distance from a given point. The center of the circle is the point equidistant from all points on the circle. A radius of a circle is a line segment with one endpoint being the center of the circle, the other endpoint being a point on the circle.
A set of points equidistant from a fixed point in a plane figure is called a circle where the distance between each of the set of the points and the fixed point forms the radius of the circle.
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| Sphere | |
|---|---|
| Surface area | 4πr2 |
| Volume | 43πr3 |
Parabola - A parabola is the set of all points (h, k) that are equidistant from a fixed line called the directrix and a fixed point called the focus (not on the line.) 2.) Axis of symmetry - A line passing through the focus and being perpendicular to the directrix.
arc. The part of the circle between any two points on the circle is called an arc.
A circle is the set of all points that are an equal, constant distance from a central point. Circles are two-dimensional figures that are not polygons.
Which of the following passes through the center of the circle and twice the length of the radius?
The diameter of a circle is a line segment that passes through the center of a circle and has two endpoints at the circumference. It is twice the length of the radius of a circle, i.e., Diameter = 2 × Radius.
A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point is a circle, and the set of points in three-space equidistant from a given point is a sphere.
A circle is a set of all points in a plane that are all an equal distance from a single point, the center. The distance from a circle's center to a point on the circle is called the radius of the circle. A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle.
A line line segment is part of a line having two points, called endpoints. It also has points between the endpoints.
A circle is a closed figure in which all the points are equidistant from the center.
a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre). Apparently it's pronounced ˈsəːk(ə)l.
The correct option is A circle. A circle is a set of points that are equidistant from a fixed point on a given surface.