Question

find the pair of angle between
x^2-7xy+6y^2​

Answer 1

Step-by-step explanation:

$\huge\bf{\mid{\overline{\underline{ANSWER:-}}\mid}}$

${x}^{2} - 7xy + 6{y}^{2}$ is a pair of straight line.

So let's compare it with its equation

${x}^{2} - 7xy + 6{y}^{2} = a{x}^{2} + 2hxy + b{y}^{2} \\ \\ a = 1 \: \: b = 6 \: \: and \: \: h = - \frac{7}{2} \\ \\ \huge{\bold{Formula:-}} \\ \\ \boxed{ \tan(\theta) = \frac{2 \sqrt{ {h}^{2} - ab}}{a + b}} \\ \\ \tan(\theta) = \frac{ 2 \sqrt{ \frac{49}{4} - 6 \times 1 }}{ 1 + 6} \\ \\ \tan(\theta) = \frac{ 2 \sqrt{\frac{25}{4}}}{7} \\ \\ \tan(\theta) = \frac{\cancel{2} \times 5}{\cancel{2} \times 7} \\ \\ \tan(\theta) = \frac{5}{7} \\ \\ \boxed{\bold{(\theta) = {\tan}^{-1} ( \frac{5}{7} )}}$