Respuesta :
Answer with explanation:
≡The given equation of line is :
x + 5 y -2=0------------(1)
⇒A line having equation, Ax +By +C=0, can be written in normal form as Follows:
[tex]\rightarrow \frac{Ax}{\sqrt{A^2+B^2}}+ \frac{By}{\sqrt{A^2+B^2}}+ \frac{C}{\sqrt{A^2+B^2}}=0[/tex]
⇒Length of Normal
[tex]=|\frac{C}{\sqrt{A^2+B^2}}|[/tex]
Let, A=Angle made by line with positive Direction of X axis.
[tex]\sin A=\frac{A}{\sqrt{A^2+B^2}}\\\\ \cos A=\frac{B}{\sqrt{A^2+B^2}}[/tex]
⇒Line, 1 in normal form can be written as:
[tex]x + 5 y=2\\\\\rightarrow\frac{x}{\sqrt{1^2+5^2}}+\frac{5 y}{\sqrt{1^2+5^2}}=\frac{2}{\sqrt{1^2+5^2}}\\\\\rightarrow\frac{x}{\sqrt{26}}+\frac{5 y}{\sqrt{26}}=\frac{2}{\sqrt{26}}[/tex]
⇒Length of Normal
[tex]=\frac{2}{\sqrt{26}}\\\\=0.40\text{approx}[/tex]
⇒Writing equation of line in slope intercept form
[tex]5 y= -x +2\\\\y=\frac{-x}{5}+\frac{2}{5}[/tex]
⇒Comparing with general slope intercept form of line:
y = m x +c,
or, y = x tan A +c
[tex]m=\tan A=\frac{-1}{5}[/tex]
