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JEE Main 2018
Conic Sections
Ellipse
Easy

Question

An ellipse, with foci at (0, 2) and (0, –2) and minor axis of length 4, passes through which of the following points?

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Solution

The problem asks us to identify which of the given points lies on an ellipse defined by its foci and minor axis length. To solve this, we first need to determine the equation of the ellipse using the provided properties.


1. Key Concepts and Formulas for an Ellipse

An ellipse is a locus of points for which the sum of the distances from two fixed points (foci) is constant. Its standard equation depends on its orientation and center.

  • Standard Equation (Centered at Origin):
    • If the major axis is along the x-axis (horizontal ellipse), the equation is x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 where a>ba > b. The

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