The angle between the lines represented by th | vedclass

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(A) Comparing the given equation with the general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$,we get $a = 1$,$2h = -1 \implies h =

Vedclass · Accepted Answer

$45$

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(A) Comparing the given equation with the general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$,we get $a = 1$,$2h = -1 \implies h = -1/2$,and $b = -6$.The formula for the angle $	heta$ between the pair of lines is given by $	an 	heta = \left| \frac{2\sqrt{h^2 - ab}}{a + b} ight|$.Substituting the values,we get $	an 	heta = \left| \frac{2\sqrt{(-1/2)^2 - (1)(-6)}}{1 + (-6)} ight|$.$	an 	heta = \left| \frac{2\sqrt{1/4 + 6}}{-5} ight| = \left| \frac{2\sqrt{25/4}}{-5} ight| = \left| \frac{2 	imes (5/2)}{-5} ight| = \left| \frac{5}{-5} ight| = |-1| = 1$.Therefore,$	heta = 	an^{-1}(1) = 45^o$.

The angle between the lines represented by the equation ${x^2} - xy - 6{y^2} - 7x + 31y - 18 = 0$ is.....$^o$

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