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Conic Section Test - 69

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Conic Section Test - 69
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    The equation of a circle passing through the vertex and the extremities of the latus rectum of the parabola y2 = 8x is
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    A man running round a race-course notes that the sum of the distance of two flsh-posts from him is always 10 metres and the distance between the flag-posts is 8 metres. The area of the path he encloses in square metres is
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    If the angle between the lines joining the end points of minor axis of an ellipse with its foci is π/2, then the eccentricity of the ellipse is
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    The eccentricity of an ellipse, with its centre at the origin, is ½. If one of the directrices is x = 4, then the equation of the ellipse is
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