Conics: Ellipses: Introduction
An ellipse, informally, is an oval or a "squished" circle. In "primitive" geometrical terms, an ellipse is the figure you can draw in the sand by the following process: Push two sticks into the sand. Take a piece of string and form a loop that is big enough to go around the two sticks and still have some slack. Take a third stick, hook it inside the string loop, pull the loop taut by pulling the stick away from the first two sticks, and drag that third stick through the sand at the furthest distance the loop will allow. The resulting shape drawn in the sand is an ellipse.
Each of the two sticks you first pushed into the sand is a "focus" of the ellipse; the two together are called "foci" (FOH-siy). If you draw a line in the sand "through" these two sticks, from one end of the ellipse to the other, this will mark the "major" axis of the ellipse. The points where the major axis touches the ellipse are the "vertices" of the ellipse. The point midway between the two sticks is the "center" of the ellipse.
Hope you like the above Equation of Ellipse with Standard Positions Expression
Please leave your comments, if you have any doubts.
An ellipse, informally, is an oval or a "squished" circle. In "primitive" geometrical terms, an ellipse is the figure you can draw in the sand by the following process: Push two sticks into the sand. Take a piece of string and form a loop that is big enough to go around the two sticks and still have some slack. Take a third stick, hook it inside the string loop, pull the loop taut by pulling the stick away from the first two sticks, and drag that third stick through the sand at the furthest distance the loop will allow. The resulting shape drawn in the sand is an ellipse.
Each of the two sticks you first pushed into the sand is a "focus" of the ellipse; the two together are called "foci" (FOH-siy). If you draw a line in the sand "through" these two sticks, from one end of the ellipse to the other, this will mark the "major" axis of the ellipse. The points where the major axis touches the ellipse are the "vertices" of the ellipse. The point midway between the two sticks is the "center" of the ellipse.
Equation of Ellipse with Standard Positions
Equation
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X2/a2+y2/b2=1, a > b
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X2/a2+y2/b2=1, a <>
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Centre
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(0,0)
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(0,0)
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Coordinate of centre.
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(a,0),(-a,0)
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(0,b),(0,-b)
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Length major axis
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2a
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2b
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2b
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2a
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Equation of major axis
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Y = 0
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X = 0
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X = 0
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Y = 0
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Equation of directrix
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X = ± a/e
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Y = ± b/e
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Eccentricity Latus rectum
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‘e’ = √(1-b2/a2) 2b2/a
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‘e’ = √(1-a2/b2) 2a2/b
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Focal distance
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a ± ex
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b ± ey
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Coordinates of foci.
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(ae , 0), (- ae , 0)
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(0 , be). (0 , - be)
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Hope you like the above Equation of Ellipse with Standard Positions Expression
Please leave your comments, if you have any doubts.
