Reduce the equation $4 x + 3 y - 24 = 0$ to the normal form and find $p, α$

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Solution

Given $4 x + 3 y - 24 = 0$
$⟹ \frac{4}{5} x + \frac{3}{5} y = \frac{24}{5}$
$⟹ x cos θ + y sin θ = \frac{24}{5}, θ = {cos}^{- 1} \frac{4}{5}$
This is in the form of $x cos α + y sin α = p$
$⟹ α = {cos}^{- 1} (\frac{4}{5}), p = \frac{24}{5}$

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Reduce the following equations to the normal form and find p and $α$ in each case :

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