The equation $2 x + 3 y = 6$ is converted into normal form then which of the following is true?

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$p = \frac{6}{\sqrt{13}}$

$\cos α = \frac{13}{\sqrt{13}}$

$\sin α = \frac{3}{\sqrt{13}}$

$\cos α = \frac{2}{\sqrt{13}}$

answer is A, B, C.

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Detailed Solution

$\begin{array}{l} x \cos α + y \sin α = p \\ 2 x + 3 y = 6 \end{array}$

Divide $\sqrt{x^{2} + 3^{2}}$ on both sides

$\begin{array}{l} \frac{2}{\sqrt{13}} x + \frac{3}{\sqrt{13}} y = \frac{6}{\sqrt{13}} \\ \cos α = \frac{2}{\sqrt{13}}, \sin α = \frac{3}{\sqrt{13}}, p = \frac{6}{\sqrt{13}} \end{array}$

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