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

  • Calculus -

    A line from (5,2) perpendicular to the curve will have the shortest distance to the curve.

    The slope of the graph is -4/3, so the normal has slope 3/4

    So, now you have a point and a slope, so the perpendicular line through (5,2) is

    y-2 = 3/4 (x-5)
    y = 3/4 x - 7/4

    These two lines intersect at (37/25,-16/25)

  • Calculus -

    Thank you for your help!

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