the foci (2 focal points) and the distance between the vertices.
The two foci are necessary to define the location of an ellipse, but the shape depends on the eccentricity, which is related to the lengths of the two axes.
The width reduces as the length increases. The changes shape of the curve is a part of a [rectangular] hyperbola.
guadrilateral
change of position, shape, or size of figure
if you multiply all the points by one you get the same points so the shape stays the same.
The two fixed points are the foci but these do not define the shape of the ellipse. You also need to know the eccentricity.
Yes, a hyperbola has co-vertices, but they are not as commonly referenced as in ellipses. The co-vertices of a hyperbola are points that lie along the transverse axis and are used to define the shape of the hyperbola. Specifically, for a hyperbola centered at the origin with a horizontal transverse axis, the co-vertices are located at ((0, \pm b)), where (b) is the distance from the center to the co-vertices. However, these points do not play a significant role in the hyperbola's properties compared to the vertices and foci.
The two foci are necessary to define the location of an ellipse, but the shape depends on the eccentricity, which is related to the lengths of the two axes.
A liquid is a state of matter that has a defined volume but no defined shape. In a liquid, particles are close enough to have a fixed volume, but not in a fixed position, allowing the substance to take the shape of its container.
An ellipse, a hyperbola.
The shape that defines the orbit of planets around the sun is an ellipse. An ellipse is a closed curve in which the sum of the distances from any point on the curve to two fixed points (foci) is constant.
To write the generic equation of a hyperbola suggested by a graph, first identify the orientation of the hyperbola (horizontal or vertical) based on its shape. The standard forms are ((x - h)^2/a^2 - (y - k)^2/b^2 = 1) for a horizontal hyperbola and ((y - k)^2/a^2 - (x - h)^2/b^2 = 1) for a vertical hyperbola, where ((h, k)) is the center, and (a) and (b) are distances that determine the shape. Use points on the graph to find the values of (h), (k), (a), and (b) to complete the equation.
a sphere
Sphere, Hyperbola and Flat.
Coplanar means "on the same plane". A plane can be a figure or shape like a rectangle. Coplanar points means points that belong on the same plane.
You are describing a sphere in three-dimensional space or a circle in two-dimensional space. In both cases, all points are equidistant from a single fixed point, known as the center. The fixed distance from the center to any point on the shape is called the radius.
One key difference between liquids and gases is their ability to maintain a fixed volume. Liquids have a definite volume, whereas gases do not have a fixed volume and will expand to fill the container they are in.