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Horizontal and Vertical Ellipse is considered one the most difficult concept.
43 Questions around this concept.
Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis. If its eccentricity is and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the end points of major and minor axes of ellipse, is
The equation of the ellipse whose axes are the axes of coordinates and which passes through the point (–3, 1) and has eccentricity is
Horizontal and Vertical Ellipse
When the major axis is along Y-axis and the minor axis is along X-axis, i.e. b > a
Then, AA’ = 2a and BB’ = 2b
The foci are S (0, be) and S’(0, be)
The equation of directrix MZ and M’Z’ are
Equation |
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Graph |
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Centre |
(0 ,0) |
(0, 0) |
Vertices |
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Length of Major Axis |
2a |
2b |
Length of Minor Axis |
2b |
2a |
Foci |
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Distance b/w foci |
2ae |
2be |
Equation of Directrices |
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Distance b/w Directrices |
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Eccentricity, e |
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Length of Latusrectum |
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Endpoint of Latusrectum |
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Focal radii |
SP+S'P = 2a |
SP+S'P = 2b |
Parametric coordinates |
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Tangent at vertices |
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