The angle between the lines represented by th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The given equation is $(x^2 + y^2)\sin 	heta + 2xy = 0$,which can be written as $(\sin 	heta)x^2 + 2xy + (\sin 	heta)y^2 = 0$.Comparing this wi

Vedclass · Accepted Answer

$\frac{\pi}{2} - 	heta$

Vedclass · Answer

(C) The given equation is $(x^2 + y^2)\sin 	heta + 2xy = 0$,which can be written as $(\sin 	heta)x^2 + 2xy + (\sin 	heta)y^2 = 0$.Comparing this with the general equation of a pair of straight lines $ax^2 + 2hxy + by^2 = 0$,we have $a = \sin 	heta$,$h = 1$,and $b = \sin 	heta$.The angle $\alpha$ between the lines is given by $	an \alpha = \left| \frac{2\sqrt{h^2 - ab}}{a + b} ight|$.Substituting the values,$	an \alpha = \left| \frac{2\sqrt{1^2 - \sin^2 	heta}}{\sin 	heta + \sin 	heta} ight| = \left| \frac{2\cos 	heta}{2\sin 	heta} ight| = |\cot 	heta|$.Since $|\cot 	heta| = 	an(\frac{\pi}{2} - 	heta)$,the angle $\alpha = \frac{\pi}{2} - 	heta$.

The angle between the lines represented by the equation $(x^2 + y^2)\sin \theta + 2xy = 0$ is

Similar Questions

If $\theta$ is an acute angle between the lines $k x^2 - 4 x y + y^2 = 0$ and $\tan \theta = \frac{1}{2}$,then the value of $k$ is

The absolute value of the tangent of the difference of the angles made by the lines $4x^2 - 24xy + 11y^2 = 0$ with the $X$-axis is

The pair of straight lines is represented by the equation $3dx^2 - 5xy + (d^2 - 2)y^2 = 0$. If the lines are perpendicular to each other,for how many values of $d$ will this condition be satisfied?

The angle between the lines represented by the equation $y^{2} \sin^{2} \theta - xy \sin^{2} \theta + x^{2}(\cos^{2} \theta - 1) = 0$ is

If the pair of straight lines $9x^2 + axy + 4y^2 + 6x + by - 3 = 0$ represents two parallel lines,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module