Where does the normal line to the parabola y=x-x^2...

Answers ( 1 )

  1. julia roger
    julia roger
    The equation of parabola is y = x - x2
    the slope of the tangent to parabola is dy/dx = 1 - 2x
    at (1,0) dy/dx = -1
    then the slope of normal is -1/-1 = 1
    then the equation of normal to the parabola at (1,0) is
       y - 0 = 1(x - 1)
    that is y = x - 1
    Now this normal will intersect parabola when
       x - 1= x -x2
    that is x2 = 1
    that is x = 1, -1
    then y = 1-1 =0 and y = -1-1= -2
    then the points of intersection of normal line with theparabola are (1,0) and (-1,-2)
    Hence the normal line at (1,0) intersects the parabola secondtime in the point (-1,-2)

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