Conic
For ancient Greek geometers such as Euclid (300 BC) and Archimedes (287-212 BC), a conic section (parabola, ellipse and hyperbola) was a curve in space, which resulted from the intersection of a plane with a cone of two branches. . , as long as the plane did not pass through the vertex of the cone
Circumference
A circumference is defined as the set of points P(x;y) in the plane equidistant from a fixed point C(h,k), (called center) at a fixed distance r (called radio).
Parable
The parabola is the set of points P (x:y) in the plane equidistant from a fixed point F (called the focus of the parabola) and of a fixed line L (called the directrix of the parabola) that does not contain F.
Ellipse
An ellipse is the set of points P(x,y) ∈ 〖IR〗^2, (geometric place) whose sum of distances to two fixed points F1 and F2 of the plane (called foci) is constant. We will call the center of the ellipse the midpoint between the foci. The line that passes through the foci cuts the ellipse at two points called vertices. The chord that joins the vertices is the major axis of the ellipse. The chord perpendicular to the major axis and passing through the center is called the minor axis of the ellipse.
Hyperbola
A hyperbola is defined as the set of points p(x,y), 〖IR〗^2 for which the difference in their distances between two different predetermined points (called foci) is, in absolute value, a constant. The line that passes through the foci cuts the hyperbola at two points called vertices. The straight segment that joins the vertices is called the transverse axis and its midpoint is the center of the hyperbola. A distinctive fact about the hyperbola is that its graph has two separate parts, called branches.
CONIC
Daniela Farfan
Created on September 16, 2023
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Transcript
Conic
For ancient Greek geometers such as Euclid (300 BC) and Archimedes (287-212 BC), a conic section (parabola, ellipse and hyperbola) was a curve in space, which resulted from the intersection of a plane with a cone of two branches. . , as long as the plane did not pass through the vertex of the cone
Circumference
A circumference is defined as the set of points P(x;y) in the plane equidistant from a fixed point C(h,k), (called center) at a fixed distance r (called radio).
Parable
The parabola is the set of points P (x:y) in the plane equidistant from a fixed point F (called the focus of the parabola) and of a fixed line L (called the directrix of the parabola) that does not contain F.
Ellipse
An ellipse is the set of points P(x,y) ∈ 〖IR〗^2, (geometric place) whose sum of distances to two fixed points F1 and F2 of the plane (called foci) is constant. We will call the center of the ellipse the midpoint between the foci. The line that passes through the foci cuts the ellipse at two points called vertices. The chord that joins the vertices is the major axis of the ellipse. The chord perpendicular to the major axis and passing through the center is called the minor axis of the ellipse.
Hyperbola
A hyperbola is defined as the set of points p(x,y), 〖IR〗^2 for which the difference in their distances between two different predetermined points (called foci) is, in absolute value, a constant. The line that passes through the foci cuts the hyperbola at two points called vertices. The straight segment that joins the vertices is called the transverse axis and its midpoint is the center of the hyperbola. A distinctive fact about the hyperbola is that its graph has two separate parts, called branches.