Define Ellipse Define Ellipse A curved line forming a closed loop, where the sum of the distances from two points (foci) to every point on the line is constant. An ellipse looks like a circle that has been squashed into an oval. Like a circle, an ellipse is a type of line. Imagine a straight line segment that is bent around until its ends join. Then shape that loop until it is an ellipse - a sort of 'squashed circle' like the one above. Things that are in the shape of an ellipse are said to be 'elliptical'. In mathematics, an ellipse (from Greek ἔλλειψις elleipsis, a "falling short") is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant. Ellipses are closed curves and are the bounded case of the conic sections, the curves that result from the intersection of a circular cone and a plane that does not pass through its apex; the other two (open and unbounded) cases are parabolas and hyperbolas. Ellipses arise from the intersection of a right circular cylinder with a plane that is not parallel to the cylinder's main axis of symmetry. Ellipses also arise as images of a circle under parallel projection and the bounded cases of perspective projection, which are simply intersections of the projective cone with the plane of projection. It is also the simplest Lissajous figure, formed when the horizontal and vertical motions are sinusoids with the same frequency.
Know More About :- Cylinders
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How ellipses are defined
An ellipse is defined by two points, each called a focus. (F1, F2 above). If you take any point on the ellipse, the sum of the distances to the focus points is constant. In the figure above, drag the point on the ellipse around and see that while the distances to the focus points vary, their sum is constant. The size of the ellipse is determined by the sum of these two distances. The sum of these distances is equal to the length of the major axis (the longest diameter of the ellipse). The two lines a and b that define the ellipse are called generator lines. Each one is sometimes called a generatrix. The position of the foci (plural of focus, pronounced 'foe-sigh') determine how 'squashed' the ellipse is. Drag F1 and F2 and see how this happens. If they are at the same location, the ellipse is a circle. A circle is, in fact, a special case of an ellipse. In the figure above, drag one focus until it is over the other.
Properties of an ellipse Center:- A point inside the ellipse which is the midpoint of the line segment linking the two foci. The intersection of the major and minor axes.
Major / minor axis:- The longest and shortest diameters of an ellipse. See Major / Minor Axis of an Ellipse. The length of the major axis is equal to the sum of the two generator lines (a and b in the diagram above).
Semi-major / semi-minor axis:- TThe distance from the center to the furthest and closest point on the ellipse. Half the major / minor axis. See Semi-major/ Semi-minor axis of an ellipse.
Foci (Focus points):- The two points that define the ellipse. See Foci of an ellipse. Learn More :- Cone
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Perimeter (circumference):- The perimeter is the distance around the ellipse. Not easy to calculate. See Perimeter of an ellipse.
Area:- The number of square units it takes to fill the region inside an ellipse. See Area enclosed by an ellipse .
Chord:- A line segment linking any two points on an ellipse. Tangent:- A line passing an ellipse and touching it at just one point. See Tangent to an Ellipse
Secant:- A line that intersects an ellipse at two points. Relation to a circle A circle is actually a special case of an ellipse. In an ellipse, if you make the major and minor axis the same length, the result is a circle, with both foci at the center.
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