Question

The normal form of the line $\frac{x}{2}+\frac{y}{3}=2$ is

• A. $\frac{3}{\sqrt{13}}x+\frac{2}{\sqrt{13}}y=\frac{12}{\sqrt{13}}$
• B. $\frac{1}{2\sqrt{13}}x+\frac{1}{3\sqrt{13}}y=\frac{2}{\sqrt{13}}$
• C. $y=\frac{-3}{2}x+6$
• D. $3x+2y=12$

Answer 1

The correct option is A $\frac{3}{\sqrt{13}}x+\frac{2}{\sqrt{13}}y=\frac{12}{\sqrt{13}}$

Given: $\frac{x}{2}+\frac{y}{3}=2$
$\Rightarrow 3x+2y=12$

Dividing with
$\sqrt{A^2+B^2}=\sqrt{3^2+2^2}=\sqrt{13}$

$\therefore$ The equation of line in normal form is
$\frac{3x}{\sqrt{13}}+\frac{2y}{\sqrt{13}}=\frac{12}{\sqrt{13}}$