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மதிப்பெல்லிப்ஸேஸ் பதிவுகள்

ஒவ்வொரு மதிப்புச் சுவாரஸ்யமும் அதன் அமைப்பு மற்றும் விளக்கம் ஒரே குறிப்பில் கொடுக்கப்பட்டுள்ளது. மிகவும் தெளிவாகவே இவை மனதில் அறிய மிகச் சிறந்த ஆவணமாகும்.

Standard form

Standard form of a horizontal ellipse: $\frac{{(x - h)}^{2}}{a^{2}} + \frac{{(y - k)}^{2}}{b^{2}} = 1$
Standard form of a vertical ellipse: $\frac{{(x - h)}^{2}}{b^{2}} + \frac{{(y - k)}^{2}}{a^{2}} = 1$

Points

Center $(h, k)$ : The point in the center of an ellipse. $h$ represents the x-coordinate and $k$ represents the y-coordinate.
Vertices: The intersections of the major axis with the ellipse.
Co-vertices: The intersections of the minor axis with the ellipse.

Lines, line segments, and axes

The major axis $(2 a)$ : the longer of the two axes that make up an ellipse. It runs from one side of the ellipse, through its center, to the other side of the ellipse at its widest point.
The minor axis $(2 b)$ : the shorter of the two axes that make up an ellipse. It runs perpendicular to the major axis, from one side of the ellipse, through its center, to the other side of the ellipse.
Semi-major axis $(a)$ : half the length of the major axis.
Semi-minor axis $(b)$ : half the length of the minor axis.
Focal length $(f)$ : the distance from the center of an ellipse to one of its foci. $f = \sqrt{a^{2} - b^{2}}$
Focal parameter $(p)$ : the distance from a focus to the corresponding directrix. $p = \frac{b^{2}}{\sqrt{a^{2} - b^{2}}}$
Directrix: Two lines outside of the ellipse that run perpendicular to the major axis and are used in conjunction with the foci to define the ellipse.
In a horizontal ellipse: $x = h \pm \frac{a^{2}}{\sqrt{a^{2} - b^{2}}}$
In a vertical ellipse: $y = k \pm \frac{a^{2}}{\sqrt{a^{2} - b^{2}}}$ .
Latus rectum: The line segments that run perpendicular to the major axis, through the foci, such that their endpoints lie on the ellipse. Their lengths equal $\frac{2 \cdot b^{2}}{a}$ .

Other properties

Area: $π \cdot a \cdot b$
Eccentricity $(e)$ : A measure of how elongated an ellipse is, defined by the following ratio: 1. The distance from the center to either focus to 2. The distance from the center to either vertex: $\frac{\sqrt{(a^{2} - b^{2})}}{a}$
The eccentricity of an ellipse is always between $0$ and $1 (0 < e < 1)$ .

சமீபத்திய தொடர்புடைய பொருள்களைத் தீர்வைச் செய்யப்பட்டது

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