The slope of a line is double the slope of another line. If tangent of

1.	The slope of a line is double the slope of another line. If tangent of the angle between them is \(\frac{1}{3}\) , find the slope of the line.
Answer» Let the slope of line be m ∴ Slope of the another line be 2m tan\(\theta\)=\(\|\frac{m_1-m_2}{1+m_1m_2}\|\) \(\frac{1}{3}\) = \(\|\frac{2m-m}{1+2m^2}\|\) \(\frac{1}{3}\) = \(\|\frac{m}{1+2m^2}\|\) 2m² + 1 = 3m 2m² – 3m + 1 = 0 (m – 1) (2m – 1) = 0 If m – 1 = 0 ⇒ m = 1 If 2m – 1 = 0 ⇒ m = \(\frac{1}{2}\) Hence, slope of lines (1 and 2) or ( \(\frac{1}{3}\) and 1)

The slope of a line is double the slope of another line. If tangent of the angle between them is \(\frac{1}{3}\) , find the slope of the line.

Answer»

Let the slope of line be m

∴ Slope of the another line be 2m

tan\(\theta\)=\(|\frac{m_1-m_2}{1+m_1m_2}|\)

\(\frac{1}{3}\) = \(|\frac{2m-m}{1+2m^2}|\)

\(\frac{1}{3}\) = \(|\frac{m}{1+2m^2}|\)

2m² + 1 = 3m

2m² – 3m + 1 = 0

(m – 1) (2m – 1) = 0

If m – 1 = 0 ⇒ m = 1

If 2m – 1 = 0 ⇒ m = \(\frac{1}{2}\)

Hence, slope of lines (1 and 2) or ( \(\frac{1}{3}\) and 1)