If the angle between the lines represented by | vedclass

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

Question

(A) The given equation is $y^2 + kxy - x^2 	an^2 A = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = -	an^2 A$,$2h =

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) The given equation is $y^2 + kxy - x^2 	an^2 A = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = -	an^2 A$,$2h = k$,and $b = 1$.The formula for the angle $	heta$ between the pair of lines is $	an 	heta = \left| \frac{2\sqrt{h^2 - ab}}{a + b} ight|$.Given $	heta = 2A$,we have $	an 2A = \left| \frac{2\sqrt{(k/2)^2 - (-	an^2 A)(1)}}{-	an^2 A + 1} ight|$.$	an 2A = \left| \frac{2\sqrt{\frac{k^2}{4} + 	an^2 A}}{1 - 	an^2 A} ight|$.We know that $	an 2A = \frac{2 	an A}{1 - 	an^2 A}$.Equating the two expressions: $\frac{2 	an A}{1 - 	an^2 A} = \frac{2\sqrt{\frac{k^2}{4} + 	an^2 A}}{1 - 	an^2 A}$.$	an A = \sqrt{\frac{k^2}{4} + 	an^2 A}$.Squaring both sides: $	an^2 A = \frac{k^2}{4} + 	an^2 A$.$\frac{k^2}{4} = 0$,which implies $k = 0$.

List-$I$	List-$II$
$(A)$ $5x^2 + 2\sqrt{7}xy - y^2 = 0$	$(I)$ $\frac{\sqrt{3}}{2}$
$(B)$ $x^2 + \sqrt{11}xy + 2y^2 = 0$	$(II)$ $\frac{1}{2\sqrt{3}}$
$(C)$ $x^2 + 2\sqrt{2}xy + y^2 = 0$	$(III)$ $\frac{1}{2}$
$(D)$ $3x^2 + 4\sqrt{2}xy + y^2 = 0$	$(IV)$ $\frac{2}{3}$
	$(V)$ $\frac{1}{\sqrt{2}}$

If the angle between the lines represented by the equation $y^2 + kxy - x^2 \tan^2 A = 0$ is $2A$,then $k =$

Similar Questions

If $\theta$ is the acute angle between the lines represented by the equation $2x^2 + 7xy + 3y^2 = 0$, then the value of $\frac{2 \cos \theta - 3 \sin \theta}{4 \sin \theta + 5 \cos \theta}$ is:

If the coordinate axes are the bisectors of the angles between the pair of lines $ax^2 + 2hxy + by^2 = 0$,where $h^2 > ab$ and $a \neq b$,then

If the angle between the pair of straight lines represented by the equation ${x^2} - 3xy + \lambda {y^2} + 3x - 5y + 2 = 0$ is ${\tan ^{ - 1}}\left( {\frac{1}{3}} \right)$,where $\lambda$ is a non-negative real number,then $\lambda$ is:

If $\theta$ is the acute angle between the pair of lines $12x^2 + 2hxy + 7y^2 = 0$ and $\tan \theta = \frac{8}{19}$,then $h =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module