If one of the lines given by the pair of line | vedclass

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

Question

(A) The equation of the pair of lines is $3x^2 + axy - 2y^2 = 0$. Dividing by $x^2$,we get $3 + a(\frac{y}{x}) - 2(\frac{y}{x})^2 = 0$. Let $m = \frac

Vedclass · Accepted Answer

$\sqrt{3}$

Vedclass · Answer

(A) The equation of the pair of lines is $3x^2 + axy - 2y^2 = 0$. Dividing by $x^2$,we get $3 + a(\frac{y}{x}) - 2(\frac{y}{x})^2 = 0$. Let $m = \frac{y}{x}$ be the slope of the lines. Then $-2m^2 + am + 3 = 0$,or $2m^2 - am - 3 = 0$. Since one line makes an angle of $60^{\circ}$ with the $x$-axis,its slope $m = 	an(60^{\circ}) = \sqrt{3}$. Substituting $m = \sqrt{3}$ into the quadratic equation: $2(\sqrt{3})^2 - a(\sqrt{3}) - 3 = 0$. $2(3) - a\sqrt{3} - 3 = 0$. $6 - a\sqrt{3} - 3 = 0$. $3 - a\sqrt{3} = 0$. $a\sqrt{3} = 3$. $a = \frac{3}{\sqrt{3}} = \sqrt{3}$.

If one of the lines given by the pair of lines $3x^2 + axy - 2y^2 = 0$ makes an angle of $60^{\circ}$ with the $x$-axis,then $a = $

Similar Questions

Vegetative propagation in $Pistia$ occurs by:

Two electric bulbs rated $P_1 \text{ watt}, V \text{ volt}$ and $P_2 \text{ watt}, V \text{ volt}$ are connected in parallel and $V \text{ volt}$ is applied to them. The total power consumed will be

The distance between the parallel lines given by $(x+7y)^2 + 4\sqrt{2}(x+7y) - 42 = 0$ is

How many species are there in the genus $Homo$?

Which of the following oxides will produce hydrogen peroxide upon reaction with dilute acid?

Vedclass Test Series

Exam Paper Generator

Online Exam Module