Given:

p = 2, sin α = \( \dfrac{1}{3}\)

We know that cos α = \( \sqrt{(1 – sin^2 α)}\)

= \( \sqrt{(1 – \dfrac{1}{9}})\)

= \( \dfrac{2\sqrt{2}}{3}\)

The equation of the line in normal form is given by

By using the formula,

x cos α + y sin α = p

Now, substitute the values, we get

\( \dfrac{x^2\sqrt{2}}{3}+\dfrac{y}{3}=2\)

\( 2\sqrt{2}x + y = 6\)

The equation of line in normal form is \( 2\sqrt{2}x + y = 6\)

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