Here you will learn how to find the coordinates of the vertices and center of ellipse formula with examples. Let’s begin – Vertices and Center of Ellipse Coordinates (i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b The coordinates of vertices are (a, 0) and (-a, 0). And the coordinates […]
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Here you will learn how to find the coordinates of the foci of ellipse formula with examples. Let’s begin – Foci of Ellipse Formula and Coordinates (i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b The coordinates of foci are (ae, 0) and (-ae, 0) (ii) For the ellipse \(x^2\over
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Here you will learn formula to find the length of major axis of ellipse and minor axis of ellipse with examples. Let’s begin – Major and Minor Axis of Ellipse (i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b Length of the major axis = 2a Length of the minor
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Here you will learn what is the formula for the length of latus rectum of ellipse with examples.. Let’s begin – Length of Latus Rectum of Ellipse (i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b Length of the Latus Rectum = \(2b^2\over a\) Equation of latus rectum is x
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Here you will learn what is the formula to find the equation of directrix of ellipse with examples. Let’s begin – Directrix of Ellipse Equation (i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b The equation of directrix is x = \(a\over e\) and x = \(-a\over e\) (ii) For
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Here you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples. Let’s begin – Eccentricity of Ellipse Formula (i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b we have, \(b^2\) = \(a^2(1 – e^2)\) \(\implies\) \(e^2\) = 1 – \(b^2\over a^2\) \(\implies\) eccentricity
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Here you will learn some ellipse examples for better understanding of ellipse concepts. Example 1 : Find the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length \(\sqrt{5}\) Solution : Here S = (2, 3) & S’ is (-2, 3) and b = \(\sqrt{5}\) \(\implies\) SS’
Here, you will learn different types of ellipse and their basic definitions with their graphs. Let’s begin – Different Types of Ellipse (a) First type of Ellipse is \(x^2\over a^2\) + \(y^2\over b^2\) = 1, where a > b (a) AA’ = Major axis = 2a (b) BB’ = Minor axis = 2b (c)
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Equation of Ellipse in Standard Form The equation of ellipse in standard form referred to its principal axes along the coordinate axes is \(x^2\over a^2\) + \(y^2\over b^2\) = 1, where a > b & \(b^2\) = \(a^2(1 – e^2)\) \(\implies\) \(a^2\) – \(b^2\) = \(a^2e^2\). where e = eccentricity (0 < e < 1)
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Equation of Tangent to Ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1 : (a) Point form : The equation of tangent to the given ellipse at its point (\(x_1, y_1\)) is \(x{x_1}\over a^2\) + \(y{y_1}\over b^2\) = 1. Note – For general ellipse replace \(x^2\) by \(xx_1\), \(y^2\) by \(yy_1\), 2x by \(x + x_1\),
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