calculus

posted by sze

Find the point on the line 3 x + 2 y - 5 =0 which is closest to the point (4,5).

  1. Arora

    Take any point on the line as (x,y)

    Now, distance between the point on the line and the given point = d

    => d^2 = (x-4)^2 + (y-5)^2

    You can treat this as a function. When d^2 is minimum, then d will be minimum too.

    function to minimize = (x-4)^2 + (y-5)^2

    But, y can be written in terms of x:
    3x + 2y = 5
    => y = (5-3x)/2

    So, by minimizing the function
    f(x) = (x-4)^2 + ((-3x-5)/2)^2
    You will get the required point.

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