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Equation of Ellipse Video Lecture | Mathematics (Maths) for JEE Main & Advanced
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FAQs on Equation of Ellipse Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. How do you find the equation of an ellipse given its foci and major axis length? |  |
Ans. To find the equation of an ellipse given its foci and major axis length, you can use the formula: $c = \sqrt{a^2 - b^2}$, where $c$ is the distance from the center to each focus, $a$ is the length of the major axis, and $b$ is the length of the minor axis. The equation of the ellipse is then $(x-h)^2/a^2 + (y-k)^2/b^2 = 1$, where $(h,k)$ is the center of the ellipse.
| 2. How do you determine the eccentricity of an ellipse? | |
Ans. The eccentricity of an ellipse can be determined by the formula $e = c/a$, where $e$ is the eccentricity, $c$ is the distance from the center to each focus, and $a$ is the length of the semi-major axis. The value of $e$ will always be less than 1 for an ellipse.
| 3. How do you find the equation of an ellipse in standard form given the endpoints of its major and minor axes? | |
Ans. To find the equation of an ellipse in standard form given the endpoints of its major and minor axes, you can use the formula $(x-h)^2/a^2 + (y-k)^2/b^2 = 1$, where $(h,k)$ is the center of the ellipse, $a$ is the length of the semi-major axis, and $b$ is the length of the semi-minor axis.
| 4. How do you determine if an ellipse is vertical or horizontal based on its equation? | |
Ans. If the coefficient of $x^2$ in the equation of an ellipse is larger than the coefficient of $y^2$, then the ellipse is horizontal. If the coefficient of $y^2$ is larger than the coefficient of $x^2$, then the ellipse is vertical.
| 5. How do you find the foci of an ellipse given its equation in standard form? | |
Ans. To find the foci of an ellipse given its equation in standard form $(x-h)^2/a^2 + (y-k)^2/b^2 = 1$, you can use the formula $c = \sqrt{a^2 - b^2}$, where $c$ is the distance from the center to each focus. The foci are located at $(h \pm c, k)$.
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Dec 25, 2024 Last updated |
Video Description: Equation of Ellipse for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation.
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