Find the point on the line y = 5x + 3 that is closest to the origin.?

1 Answer

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  • let the point (m , n) on the line y = 5x + 3 is closest to origin (0,0)

    substituting x = m and y = n in eqn of line

    n = 5m + 3

    so The point is (m . 5m + 3)

    The distance, s between [ m , (5m + 3) ] and (0, 0) is

    s = √[m^2 + (5m+3)^2 ]

    = √(m^2 + 25m^2 + 30m + 9)

    = √(26m^2 + 30m + 9)

    differentiate and equate it to zero

    (1/2)[ 52m + 30] / √(26m^2 + 30m + 9) = 0

    => 52m + 30 = 0

    m = -30 / 52

    = -15/26

    n = 5m + 3

    = -(75/26) + 3

    = 3/26

    The closest point to origin = (-15/26, 3/26)

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