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Conic Sections ...

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  • Question 1
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    Consider
    the set of hyperbola $$xy = {\text{ }}K,{\text{ K}} \in {\text{R,}}$$  let $${e_1}$$  be eccentricity
    when $$K = \sqrt {2017} $$  and $${e_2}$$ be the
    eccentricity when $$K = \sqrt {2018} $$ , then $${e_1} - {e_2}$$   is equal to 

  • Question 2
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    The centre of a circle is $$(2, -3)$$ and the circumference is $$10\pi$$. Then, the equation of the circle is

  • Question 3
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    A conic $$C$$ passes through the points $$(2,4)$$ and is such that the segment of any of its tangents at any point contained between the co-ordinate axis is biscected at the point of tangency. Let $$S$$ denotes circle described on the foci $${F_1}$$ and $${F_2}$$ of the conic $$C$$ as diameter.
    Equation of the circle $$S$$ is

  • Question 4
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    The centre of a circle passing through the point $$(0,0),(1,0)$$ and touching the circle $$x^{2}+y^{2}=9$$ is ?

  • Question 5
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    If the centroid of an equilateral triangle  $$(1,1)$$ and its one vertex is $$(-1,2)$$ , then the equation of the circumcircle is 

  • Question 6
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    The focus of extremities of the latus rectum of the family of the ellipse  $${b^2}{x^2} + {a^2}{y^2} = {a^2}{b^2}{\text{ is }}\left( {b \in R} \right)$$ 

  • Question 7
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    Circles are drawn passing through the origin $$O$$ to intersect the coordinate axes at point $$P$$ and $$Q$$ such that $$m$$. $$PO+n.OQ=k$$, then the fixed point satisfy all of them, is given by

  • Question 8
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    The vertex $$A$$ of the parabola $${y}^{2}=4ax$$ is joined to any point $$P$$ on it and $$PQ$$ is drawn at right angles to $$AP$$ to meet the axis in $$Q$$. Projection of $$PQ$$ on the axis is equal to

  • Question 9
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    If equation $$(5x-1)^{2}+(5y-2)^{2}=(\lambda^{2}-2\lambda+1)(3x+4y-1)^{2}$$ represents an ellipse, then $$\lambda \in$$

  • Question 10
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    The locus of the mid points of the portion of the tangents to the ellipse intercepted between the axes

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