Multiple Choice Questions on If a line 3x ndash y 2 intersects ellipse x2 8 y2 4 1 at points A amp B then find coo........... for NDA Exam Preparation

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Multiple Choice Questions

If a line 3x ndash y 2 intersects ellipse x2 8 y2 4 1 at points A amp B then find coo...........

Mathematics (NDA) Coordinate Geometry
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    If a line 3x – y = 2 intersects ellipse x2/8  + y2/4  =1  at points A & B, then find coordinates of the point of intersection of tangents at points A & B ?

    (-19/104  ,-2)

    Incorrect Answer

    (-19/114  ,2)

    Incorrect Answer

    (-19/114  ,-2)

    Correct Answer

    (11/114  ,-2)

    Incorrect Answer
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    Explanation:

    line 3x – y = 2

    ellipse x2/8  + y2/4  =1 

     x2/8  + (3x-2)2/4  =1

    x2/8  +(9x2 +4-12x)/4   =1

    x2  +18x2 +8-24x =8

    19x2 -24x=0

    X=0  ,x=24/19

    Point (0,-2),(24/19  ,34/19)

    Tangents equation (0,-2)

    x2/8  + y2/4  =1 

    -2y/4  =1

    Y=-2

    Tangent At (24/19  ,34/19)

    24x/152  +34y/76   =1

    Finding intersection of 24x/152  =1-78/76

                   =-1/38

    X=-76/456

        =-19/114

    Point (-19/114  ,-2)

    By: bhavesh kumar singh
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