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Introduction to Ellipse (Part - 7) - Conic Sections, Math, Class 11 Video Lecture

FAQs on Introduction to Ellipse (Part - 7) - Conic Sections, Math, Class 11 Video Lecture

1. What are conic sections?
Ans. Conic sections are the curves formed by the intersection of a plane with a cone. The four types of conic sections are the circle, ellipse, parabola, and hyperbola. Each type has its own unique properties and equations.
2. How is an ellipse defined in mathematics?
Ans. In mathematics, an ellipse is defined as the set of all points in a plane such that the sum of the distances from any point on the ellipse to two fixed points (called the foci) is constant. The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter.
3. What is the general equation of an ellipse?
Ans. The general equation of an ellipse with its center at the origin (0,0) is given by x^2/a^2 + y^2/b^2 = 1, where a is the length of the semi-major axis and b is the length of the semi-minor axis. This equation represents an ellipse with its major axis parallel to the x-axis.
4. How is the eccentricity of an ellipse defined?
Ans. The eccentricity of an ellipse is a measure of how elongated or stretched out the ellipse is. It is defined as the ratio of the distance between the foci to the length of the major axis. The eccentricity of an ellipse is always between 0 and 1, where 0 represents a circle and 1 represents a highly elongated ellipse.
5. What is the focus-directrix property of an ellipse?
Ans. The focus-directrix property of an ellipse states that for any point on an ellipse, the distance from that point to the focus is equal to the perpendicular distance from that point to the directrix. This property helps in defining and understanding the geometric properties of ellipses.
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