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Ellipse: Eccentricity Standard Equations of Ellipse Latus Rectum Video Lecture | Mathematics (Maths) for JEE Main & Advanced
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FAQs on Ellipse: Eccentricity Standard Equations of Ellipse Latus Rectum Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. What is the eccentricity of an ellipse? |  |
The eccentricity of an ellipse is a measure of how elongated or stretched out the ellipse is. It is a number between 0 and 1, where 0 represents a circle and 1 represents a completely stretched out ellipse.
| 2. How can I find the standard equations of an ellipse? | |
To find the standard equations of an ellipse, you need the coordinates of the center of the ellipse, the lengths of the major and minor axes, and the orientation of the ellipse. The standard equations for an ellipse with center (h, k) and major and minor axes of lengths 2a and 2b are: $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ for a horizontally oriented ellipse, and $\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$ for a vertically oriented ellipse.
| 3. What is the latus rectum of an ellipse? | |
The latus rectum of an ellipse is a line segment that passes through one of the foci of the ellipse and is perpendicular to the major axis. Its length is equal to the distance between the two directrices of the ellipse.
| 4. How can I calculate the length of the latus rectum of an ellipse? | |
The length of the latus rectum of an ellipse can be calculated using the formula 2b^2/a, where a is the length of the semi-major axis and b is the length of the semi-minor axis of the ellipse.
| 5. Can the eccentricity of an ellipse be greater than 1? | |
No, the eccentricity of an ellipse cannot be greater than 1. The eccentricity is defined as the ratio of the distance between the center and a focus of the ellipse to the length of the semi-major axis. Since the distance between the center and a focus cannot be greater than the length of the semi-major axis, the eccentricity is always less than or equal to 1.
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Nov 22, 2024 Last updated |
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