Here you will learn what is the formula to find the length of latus rectum of hyperbola with examples. Let’s begin – Length of Latus Rectum of Hyperbola Formula (i) For the hyperbola \(x^2\over a^2\) – \(y^2\over b^2\) = 1 Length of Latus Rectum = \(2b^2\over a\) (ii) For the hyperbola -\(x^2\over a^2\) + \(y^2\over …
Here you will learn what is the eccentricity of hyperbola formula and how to find eccentricity with examples. Let’s begin – Eccentricity of Hyperbola Formula (i) For the hyperbola \(x^2\over a^2\) – \(y^2\over b^2\) = 1 Eccentricity (e) = \(\sqrt{1 + {b^2\over a^2}}\) (ii) For the hyperbola -\(x^2\over a^2\) + \(y^2\over b^2\) = 1 Eccentricity …
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Here you will learn formula to find the equation of directrix of hyperbola with examples. Let’s begin – Directrix of Hyperbola Equation (i) For the hyperbola \(x^2\over a^2\) – \(y^2\over b^2\) = 1 The equation of directrix is x = \(a\over e\) and x = \(-a\over e\) (ii) For the hyperbola -\(x^2\over a^2\) + \(y^2\over …
Here you will learn how to find the coordinates of the foci of hyperbola with examples. Let’s begin – Foci of Hyperbola Coordinates (i) For the hyperbola \(x^2\over a^2\) – \(y^2\over b^2\) = 1 The coordinates of foci are (ae, 0) and (-ae, 0). (ii) For the conjugate hyperbola -\(x^2\over a^2\) + \(y^2\over b^2\) = …
Here you will learn formula to find the length of conjugate axis and transverse axis of hyperbola with examples. Let’s begin – Conjugate and Transverse Axis of Hyperbola (i) For the hyperbola \(x^2\over a^2\) – \(y^2\over b^2\) = 1 The length of the transverse axis = 2a And the length of the conjugate axis = …
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Here you will learn how to find the coordinates of the vertices and center of hyperbola formula with examples. Let’s begin – Vertices and Center of Hyperbola Coordinates (i) For the hyperbola \(x^2\over a^2\) – \(y^2\over b^2\) = 1 The coordinates of vertices are (a, 0) and (-a, 0). And the coordinates of center is …
Here you will learn some hyperbola examples for better understanding of hyperbola concepts. Example 1 : If the foci of a hyperbola are foci of the ellipse \(x^2\over 25\) + \(y^2\over 9\) = 1. If the eccentricity of the hyperbola be 2, then its equation is : Solution : For ellipse e = \(4\over 5\), …
Here, you will learn equation of asymptotes of hyperbola and how to find the asymptotes of the hyperbola and the director circle of hyperbola. Let’s begin – Equation of Asymptotes of hyperbola If the length of the perpendicular let fall from the point on the hyperbola to a straight line tends to zero as the …
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Here, you will learn what is rectangular hyperbola and parametric equation of rectangular hyperbola with example. Let’s begin – Rectangular Hyperbola The particular kind of the hyperbola in which the length of it’s transverse axis and conjugate axis are equal is called rectangular hyperbola. The eccentricity of the rectangular hyperbola is \(\sqrt{2}\) and the length …
Equation of Tangent to Hyperbola \(x^2\over a^2\) – \(y^2\over b^2\) = 1 (a) Point form : The equation of tangent to the given hyperbola at its point (\(x_1, y_1\)) is \(x{x_1}\over a^2\) – \(y{y_1}\over b^2\) = 1 Example : Find the equation of tangent to the hyperbola \(16x^2\) – \(9y^2\) = 144 at (5, 16/3). …
