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Hyperbola : Eccentricity Standard Equations Latus Rectum Video Lecture | Mathematics (Maths) Class 11 - Commerce

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FAQs on Hyperbola : Eccentricity Standard Equations Latus Rectum Video Lecture - Mathematics (Maths) Class 11 - Commerce

1. What is the standard equation of a hyperbola with eccentricity?
Ans. The standard equation of a hyperbola with eccentricity is given by: $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ for a hyperbola with horizontal transverse axis, and $\dfrac{y^2}{a^2} - \dfrac{x^2}{b^2} = 1$ for a hyperbola with vertical transverse axis.
2. How do you find the eccentricity of a hyperbola?
Ans. The eccentricity of a hyperbola can be found using the formula $e = \sqrt{1 + \dfrac{b^2}{a^2}}$, where $a$ is the distance from the center to a vertex, and $b$ is the distance from the center to a co-vertex.
3. What is the significance of eccentricity in a hyperbola?
Ans. The eccentricity of a hyperbola determines its shape and characteristics. It represents how "stretched out" the hyperbola is, with higher eccentricity values indicating a more elongated shape. The eccentricity also affects the distance between the foci and the vertices of the hyperbola.
4. What are the latus rectum of a hyperbola?
Ans. The latus rectum of a hyperbola is a line segment that passes through the foci and is parallel to the transverse axis. It is the segment connecting the points on the hyperbola that are closest to the foci. The length of the latus rectum can be found using the formula $L.R. = \dfrac{2b^2}{a}$, where $a$ is the distance from the center to a vertex, and $b$ is the distance from the center to a co-vertex.
5. How does the eccentricity affect the latus rectum of a hyperbola?
Ans. The eccentricity of a hyperbola does not directly affect the length of the latus rectum. The length of the latus rectum is solely determined by the distances $a$ and $b$. However, the eccentricity indirectly influences the shape of the hyperbola, which in turn affects the position and orientation of the latus rectum.
75 videos|238 docs|91 tests

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