Distance of a Point From a Line

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  • Q1

    The distance between the parallel lines y = 2x + 4
    and
    6x = 3y + 5 is

    Marks:1
    Answer:

    Explanation:

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  • Q2

    Let the algebraic sum of the perpendicular distances from the points (2, 0), (0, 2), (1, 1 ) to a variable line be zero, then the line passes through a fixed point whose coordinates are

    Marks:1
    Answer:

    (1, 1).

    Explanation:

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  • Q3

    Two lines are given (x – 2y)2 + k (x – 2y) = 0. The value of k, so that the distance between them is 3, is

    Marks:1
    Answer:

    k = 35.

    Explanation:

    The lines are given by

    (x – 2y)2 + k (x – 2y) = 0 

    (x - 2y)(x - 2y + k) = 0  

    That is x  – 2y = 0 and x – 2y + k = 0

    These are parallel. The distance between the two lines

      

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  • Q4

    The equation of a straight line, which passes through the point (a, 0) and whose perpendicular distance from the point (2a, 2a) is a, is

    Marks:1
    Answer:

    3x – 4y – 3a = 0 and x – a = 0.

    Explanation:

    Equation of line passing through (a, 0) is y = m(x – a)
     mx - y - ma = 0                                            ...(i)
    Its distance from the point (2a, 2a) is
       |(2am - 2a - ma)/(m2 + 1)| = a (given)

     (m - 2)2 = (m2 + 1)

      m2 - 4m + 4 = m2 + 1 

     

     - 4m + 3 = 0

     m = 3/4, .

    [If a = 0 then one root of ax2 + bx + c = 0 is infinite]

    This result must be taken into care otherwise one root will be lost.

    The required equation of lines is, from (i)

              3x – 4y – 3a = 0

    and       y = (x – a)
    x – a = 0.
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  • Q5

    The distance of the line 2x + y = 3 from the point (–1, 3) is

    Marks:1
    Answer:

    Explanation:

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