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Menaechmus was the first to study the ellipse. After then, Euclid looked into it and wrote about it. Apollonius came up with the name. The focus of an ellipse and the directrix of an ellipse were both considered by Pappus. In 1602 Kepler hypothesised that Mars’ orbit was oval and researched it until he established that the ellipse with the Sun was at one focus. Kepler also coined the term “focus,” which he published in 1609. Halley demonstrated in 1705 that the comet named after him was also moving in an elliptical orbit around the Sun. An oblate spheroid is formed by rotating an elliptical around its minor axis, and a prolate spheroid is formed by rotating an ellipse around its major axis.
The shape of an Ellipse
An ellipse is a two-dimensional shape specified along its axes in geometry. When a cone is intersected by a plane at an angle to its base, an ellipse is created.
It has two main sites of interest. For all points in a curve, the total of the two distances to the focal point is always constant.
A circle is an ellipse in which the foci are all at the same location, which is the circle’s centre.
The Ellipse’s Most Important Characteristics
1. Center: The centre is the point where the main and minor axes intersect.
2. Focus: The focus is the fixed point on the Ellipse.
3. Major Axis: The Ellipse’s largest diameter.
4. Minor Axis: The Ellipse’s shortest diameter.
5. Directrix: The directrix is Ellipse’s fixed straight line.
6. Eccentricity: The Ellipse’s constant ratio, indicated by e. e1.
7. Tangent: A tangent is a line that only touches the Ellipse at one point.
The chord is the line that connects any two locations on the Ellipse.
An ellipse’s focal point
1. Foci are the specific points that define an ellipse and are made up of two focus points.
2. The ellipse is defined as the collection or locus of all points on a plane whose distances from two fixed points termed Focus are the sum of their distances has a consistent emphasis.
3. The principal axis is always where the foci are.
4. Both the focus and the centre are at the same distance.
5. Linear Eccentricity refers to the distance between the centre and any of the focus points.
What Is Ellipse Eccentricity?
The focus and the directrix of the ellipse are two key terms to understand before discussing eccentricity. The eccentricity of a conic section is defined as the ratio of the distance from the fixed point – focus – to the distance from the fixed-line – directrix being a constant number for any point on it.
Solving Previous Year’s Question Papers Has Its Advantages
Familiarize yourself with the exam format.
The exam is difficult; JEE Main is a national level exam with a high degree of competition. As a result, knowing the specific exam pattern is critical for a candidate to begin studying.
More effective time management
Candidates are expected to manage their time wisely once they begin attempting the previous year’s question paper. Solving past years’ JEE Main test papers has a number of advantages.
Furthermore, it is thought to be a really excellent practice. It not only improves speed, but also encourages accuracy over time. Furthermore, when taking any exam, time is critical, and in the case of JEE Main, it is one of the most important factors.
Practice till you’re perfect
Long has it been said that practice makes perfect. As a result, everything that has been practised for a long period will yield superior outcomes. As a result, when applicants spend a significant amount of time practising questions from past years, they are automatically predicted to achieve a high percentile.
Furthermore, the prior year’s JEE Mains practise can only aid in determining the level of preparation. Candidates can now measure their level of preparedness with ease.
Furthermore, candidates might concentrate on minimising the preparation gap based on their evaluation.
Examine your strengths and weaknesses.
Read the question paper carefully as you go through it. Mark the questions that you know the answers to and leave the rest blank. It is the most effective method for determining the answers to both known and unknown questions.
Candidates may now readily draw out the areas where they need to focus their attention and get down to business.
In addition, below are the advantages of solving past years’ JEE questions. The main question papers demonstrate that the candidates have learned to categorise exams as challenging, moderate, or easy. As a result, they may now quickly begin revised preparations.
As a Conic Section, Ellipse
Ellipse is a type of conic section, meaning it may be made from a cone’s cross-section. A circle is formed by cutting a cone parallel to its base. However, if you cut the cone at an angle through its curved face, you’ll get an ellipse, as seen in the illustration below. An ellipse is a plane section of a cone that does not contain the cone’s apex and has a slope less than the slope of the cone’s lines.
Also read: JEE Advanced Sample Papers
FAQs
In JEE, what is an ellipse?
An ellipse is a geometrical shape in which each point is the same total distance from the two fixed points in a conic section. For JEE aspirants, the previous year's question with solutions on Ellipse is a valuable resource. Students will come across questions from prior JEE examinations while studying this part.
What is the ellipse equation, and what are its properties?
The concept of an ellipse is crucial for the JEE exam. The set of all points on a plane whose distances from two points add up to a constant is called an ellipse. We will come across definitions, ellipse equations, and properties in this article, which will aid students in gaining a thorough understanding of the issue.
