Find the equations of the tangent and normal to the parabola y² = 4ax at the point (at², 2at).

Question

Find the equations of the tangent and normal to the parabola y² = 4ax at the point (at², 2at).

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3 weeks 2021-10-04T00:56:15+00:00 1 Answer 0 views 0

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  1. Emma
    0
    2021-10-04T00:57:59+00:00

    HELLO DEAR,

    given curves are y² = 4ax at point (at² , 2at).

    now, 2y * dy/dx = 4a

    dy/dx = 2a/y

    the slope of tangent at point at point (at² , 2at) is

    Equation of the tangent at (x1 , y1) where slope is m is given by y − y1 = m(x−x1)

    where, m = dy/dx

    hence, the equation of tangent is:

    y – 2at = dy/dx(x – at²)

    y – 2at = 1/t(x – at²)

    yt – 2at² = x – at²

    x – yt + at² = 0

    Equation of the normal at (x1 , y1) where slope is m is given by y − y1 = -1/m(x−x1)

    where, m = dy/dx ,

    hence, equation of normao is:

    y – 2at = -1/(1/t)(x – at²)

    y – 2at = -xt + at³

    y + xt = at³ + 2at.

    I HOPE ITS HELP YOU DEAR,

    THANKS

    plz mark me as BRILLIANT ❤️…

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