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CONIC SECTIONS - Coggle Diagram

- - - - A set of all points in the plane whose distance from a fixed point is constant
    - - x^2 + y^2 = r^2 when the center is at the origin.
      - (x-h)^2+(y-k)^2 = r^2 when the center is not at the origin.
    - - Bottle Caps
      - Rim of a cone glass
      - Wheels
    - - Center: Equidistant point of the Circle.
      - Radius: Distance from the Center to the Circumference.
      - Circumference: Distance around the Circle.
  - - - a symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one.
    - - Focus and Parabola - What are a parabola's focus and directrix? Typically speaking, parabolas are the graphs of quadratic functions. They may alternatively be thought of as the collection of all points whose separation from the focus is the same as their separation from a certain line (the directrix).
      - Vertex - The point at which a parabola crosses its axis of symmetry is known as the vertex. The lowest point on the graph, or the point at the base of the "U"-shape, will be the vertex if the coefficient of the x2 term is positive.
      - The Axis - The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.
      - The latus rectum of the parabola is the focal chord drawn perpendicular to the parabola's axis. The directrix of a parabola and the latus rectum are parallel. The latus rectum of the parabola y2=4axy2=4ax is 4a units long, and its endpoints are (a, 2a), and (a, -2a).
      - Focal Length - The focal length of the parabola is denoted by the positive integer a. Where (p,q) is the vertex and an is the focal length, (xp)2=4a(yq), with a>0.
    - - The shape of the banana, roller coaster, bridges, arch, rainbow, and etc..
  - - - An ellipse is a set of all coplanar points such that the sum of its distances from two fixed points is constant.
    - - Focus/Foci: The two fixed points is the focus of the ellipse, the plural form of focus is foci.
      - Vertices: Points of intersection of the ellipse and the line passing through the two foci F1 and F2.
      - Major axis: The line segment connecting V1 and V2 passing through the foci.
      - Center: The midpoint of the V1 and V2.
      - Minor axis: The line segment perpendicular to the major axis which passes through the center.
      - Co - vertices: The two points on the ellipse which intersect the minor axis.
    - - The orbits of planets, satellites, moons, and comets, as well as the shapes of football and a tilted glass of water.
  - - - A hyperbola is a two-branched open curve formed by the intersection of a plane and both sides of a double cone. The plane does not have to be parallel to the cone's axis; nevertheless, it will be symmetrical if it is.
    - - Foci - The foci are two fixed points that form the hyperbola.
      - Focal length - The focal length is the measurement of the distance between two foci. This length equals 2c.
      - Transverse axis - This axis represents the link between the two foci. The hyperbola equation is used to determine the location of the transverse axis. When the x term is positive, the transverse axis is on the x-axis or parallel to it. When the y term is positive, the transverse axis is on the y-axis or parallel to it.
      - Conjugate axis - The imaginary axis is another name for the conjugate axis. This axis runs orthogonal to the transverse axis and divides it in half.
      - Axes of symmetry - The hyperbola has two axes of symmetry, one horizontal and one vertical. These axes are parallel to the transverse and conjugate axes.
      - Center - The center is the point at where the hyperbola's two lines of symmetry intersect. The center is also the point at where the two asymptotes intersect.
      - Vertices - The vertices are the transverse axis's ends. These are the points formed by the intersection of the hyperbola with the transverse axis.
      - Semi-major axis - The semi-major axis is a line segment that connects the hyperbola's center to a vertex.
      - Semi-minor axis - The semi-minor axis is a perpendicular line segment to the semi-major axis.
      - Asymptotes - The behavior of hyperbolas is represented by the asymptotes. The asymptotes are the lines that are very close to the hyperbola's branches but never touch it.
    - - Eye glasses, Guitars, Telescopes, and Televisions etc.