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

(D) The given equation is $y^{2} \sin^{2} 	heta - xy \sin^{2} 	heta + x^{2}(\cos^{2} 	heta - 1) = 0$. Since $\cos^{2} 	heta - 1 = -\sin^{2} 	heta

Vedclass · Accepted Answer

$\frac{\pi}{2}$

Vedclass · Answer

(D) The given equation is $y^{2} \sin^{2} 	heta - xy \sin^{2} 	heta + x^{2}(\cos^{2} 	heta - 1) = 0$. Since $\cos^{2} 	heta - 1 = -\sin^{2} 	heta$,the equation becomes $y^{2} \sin^{2} 	heta - xy \sin^{2} 	heta - x^{2} \sin^{2} 	heta = 0$. Dividing by $\sin^{2} 	heta$ (assuming $\sin^{2} 	heta 
eq 0$),we get $y^{2} - xy - x^{2} = 0$. For a general second-degree equation $ax^{2} + 2hxy + by^{2} = 0$,the angle $\phi$ between the lines is given by $	an \phi = \left| \frac{2\sqrt{h^{2} - ab}}{a + b} ight|$. Here,$a = -1$,$2h = -1$ (so $h = -1/2$),and $b = 1$. Since $a + b = -1 + 1 = 0$,the sum of the coefficients of $x^{2}$ and $y^{2}$ is zero. This implies that the lines are perpendicular to each other. Therefore,the angle between the lines is $\frac{\pi}{2}$.

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

Similar Questions

If $\theta$ is the acute angle between the pair of lines $H \equiv ax^2 - xy + by^2 = 0$,$\tan \theta = 5$ and $(1, -1)$ is a point on $H = 0$,then $a^2 + ab + b^2 =$

The angle between the pair of straight lines $x^2 + 4y^2 - 7xy = 0$ is

The number of values of $a$ for which the pair of lines represented by $3ax^2 + 5xy + (a^2 - 2)y^2 = 0$ are at right angles to each other,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 lines represented by the equation $x^2 + 2\sqrt{3}xy + 3y^2 - 3x - 3\sqrt{3}y - 4 = 0$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module