Question

find the acute angle between the lines 12x-4y=5 and 4x+2y=7​

Answer 1

Answer:

The acute angle between the given straight lines is 45 degrees

Step-by-step explanation:

$Given\;lines\:are\\\\12x-4y-5=0\;\;and\;\;4x+2y-7=0$

$\text{Slope of 12x-4y-5=0 is }m_1=\frac{-12}{-4}=3$

$\text{Slope of 4x+2y-7=0 is }m_2=\frac{-4}{2}=-2$

$\text{Let \theta be the angle between the given straight lines}$

$Then\;\\\\\bf\;tan\,\theta=|\frac{m_1-m_2}{1+m_1\,m_2}|$

$\implies\;tan\,\theta=|\frac{3+2}{1+(3)(-2)}|$

$\implies\;tan\,\theta=|\frac{5}{1-6}|$

$\implies\;tan\,\theta=|\frac{5}{-5}|$

$\implies\;tan\,\theta=|-1|$

$\implies\;tan\,\theta=1$

$\implies\bf\theta=45^{\circ}$

Answer 2

Answer:

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