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Ellipse is one of the easiest topics in the Conic Sections of Co-ordinate Geometry in Mathematics.
"Ellipse" is defined as the locus of a point which moves such that the ratio of its distance (Eccentricity) from a fixed point (Locus) and a fixed line (Directrix) is less than one i.e. a point moves such that its distance from a fixed point is always less than the distance from a fixed line, we get a different types of curve for one value of eccentricity, which are similar for all values of eccentricity less than one. Thus curve looks like a circle but it is not exactly a circle. Rather it is more like the edges of an egg. And if we plot the movement of the Earth and other planets around the Sun, it is the same curve satisfying the above condition of eccentricity less than one. This beautiful curve has been named as "Ellipse".
In this chapter we will discuss in detail the nature/properties of this beautiful and important curve. As you will see, the curve is symmetrical about two axes. We will study the standard form of ellipse where the X and y-axes will be taken as these axes. The main emphasis in this chapter should be on learning the properties ofellipse. The judgement of using parametric co-ordinates, which can reduce the complexity of the problem, should also be learnt.
Ellipse is important from the perspective of scoring high in IIT JEE as it fetches 1-2 questions in most of the engineering examination. You are expected to do all the questions based on this to remain competitive in IIT JEE examination. It is very important to master these concepts at early stage as this forms the basis of your preparation for IIT JEE, AIEEE, DCE, EAMCET and other engineering entrance examinations.
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