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# parts of conic sections

A vertex, which is the point at which the curve turns around, A focus, which is a point not on the curve about which the curve bends, An axis of symmetry, which is a line connecting the vertex and the focus which divides the parabola into two equal halves, A radius, which the distance from any point on the circle to the center point, A major axis, which is the longest width across the ellipse, A minor axis, which is the shortest width across the ellipse, A center, which is the intersection of the two axes, Two focal points —for any point on the ellipse, the sum of the distances to both focal points is a constant, Asymptote lines—these are two linear graphs that the curve of the hyperbola approaches, but never touches, A center, which is the intersection of the asymptotes, Two focal points, around which each of the two branches bend. In the next figure, each type of conic section is graphed with a focus and directrix. Namely; The rear mirrors you see in your car or the huge round silver ones you encounter at a metro station are examples of curves. All hyperbolas have two branches, each with a focal point and a vertex. In the case of an ellipse, there are two foci, and two directrices. A curve, generated by intersecting a right circular cone with a plane is termed as ‘conic’. The types of conic sections are circles, ellipses, hyperbolas, and parabolas. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. It has distinguished properties in Euclidean geometry. The degenerate form of the circle occurs when the plane only intersects the very tip of the cone. These are the distances used to find the eccentricity. Conic consist of curves which are obtained upon the intersection of a plane with a double-napped right circular cone. In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. In the next figure, a typical ellipse is graphed as it appears on the coordinate plane. They may open up, down, to the left, or to the right. In this way, increasing eccentricity can be identified with a kind of unfolding or opening up of the conic section. The topic of conic sections has been around for many centuries and actually came from exploring the problem of doubling a cube. An equation has to have x2 and/or y2 to create a conic. The conics form of the equation has subtraction inside the parentheses, so the (x + 3)2 is really (x – (–3))2, and the vertex is at (–3, 1). Conic sections can be generated by intersecting a plane with a cone. A conic section is the plane curve formed by the intersection of a plane and a right-circular, two-napped cone. It also shows one of the degenerate hyperbola cases, the straight black line, corresponding to infinite eccentricity. Some examples of degenerates are lines, intersecting lines, and points. A conic section is a curve on a plane that is defined by a 2 nd 2^\text{nd} 2 nd-degree polynomial equation in two variables. In the next figure, four parabolas are graphed as they appear on the coordinate plane. So to put things simply because they're the intersection of a plane and a cone. If neither x nor y is squared, then the equation is that of a line. The circle is type of ellipse, and is sometimes considered to be a fourth type of conic section. Also, let FM be perpendicular to t… Thus, like the parabola, all circles are similar and can be transformed into one another. These distances are displayed as orange lines for each conic section in the following diagram. Parts of conic sections: The three conic sections with foci and directrices labeled. If $e = 1$, the conic is a parabola, If $e < 1$, it is an ellipse, If $e > 1$, it is a hyperbola. This means that, in the ratio that defines eccentricity, the numerator is less than the denominator. For the parabola, the standard form has the focus on the x-axis at the point (a, 0) and the directrix is the line with equation x = −a. A parabola has one focus about which the shape is constructed; an ellipse and hyperbola have two. For a parabola, the ratio is 1, so the two distances are equal. Conic Sections and Standard Forms of Equations A conic section is the intersection of a plane and a double right circular cone . Two massive objects in space that interact according to Newton’s law of universal gravitation can move in orbits that are in the shape of conic sections. If α<β<90o, the conic section so formed is an ellipse as shown in the figure below. Apollonius of Perga ( circa 200 B.C these are the curves which can be thought of cross-sections. 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