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Calculus

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Write the equation 4x + 5y – 3 = 0 in normal form. Then, find the length of the normal and the angle it makes with the positive x–axis.

  • Calculus - ,

    From
    4x + 5y – 3 = 0
    Divide all coefficients by sqrt(4^2+5^2) to get
    4x/sqrt(41) +5y/sqrt(41) - 3/sqrt(41) = 0
    where
    3/sqrt(41) = length of normal
    cos(θ)=4/sqrt(41), and
    sin(θ)=5/sqrt(41)

    Note: the normal form is given by:
    x cos(θ) + y sin(θ) - p =0
    where |p|=length of normal.

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