One line of the pair of lines x^2+xy-2y^2=0 i | vedclass

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

Question

(C) The given pairs of lines are $x^2+xy-2y^2=0$ and $2x^2+5xy-3y^2=0$. Factoring the first pair: $(x+2y)(x-y)=0$. The lines are $L_1: x+2y=0$ and $L_

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) The given pairs of lines are $x^2+xy-2y^2=0$ and $2x^2+5xy-3y^2=0$. Factoring the first pair: $(x+2y)(x-y)=0$. The lines are $L_1: x+2y=0$ and $L_2: x-y=0$. Factoring the second pair: $(2x-y)(x+3y)=0$. The lines are $L_3: 2x-y=0$ and $L_4: x+3y=0$. We check for perpendicularity: The slope of $L_1$ is $m_1 = -1/2$. The slope of $L_3$ is $m_3 = 2$. Since $m_1 	imes m_3 = -1$,$L_1$ and $L_3$ are perpendicular. The remaining lines are $L_2: x-y=0$ and $L_4: x+3y=0$. The combined equation of these two lines is $(x-y)(x+3y)=0$. Expanding this: $x^2+3xy-xy-3y^2 = x^2+2xy-3y^2=0$. Comparing this with $ax^2+2hxy+by^2=0$,we get $a=1$,$2h=2$,and $b=-3$. Therefore,$a+2h+b = 1+2-3 = 0$.

One line of the pair of lines $x^2+xy-2y^2=0$ is perpendicular to one line of the pair of lines $3y^2-5xy-2x^2=0$. If the combined equation of the two lines other than those two perpendicular lines is $ax^2+2hxy+by^2=0$,then $a+2h+b=$

Similar Questions

If the system of equations $ax + y + z = 0$,$x + by + z = 0$,and $x + y + cz = 0$ $(a, b, c \neq 1)$ has a non-trivial solution,then the value of $\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$ is:

If $3 \cos x \neq 2 \sin x$,then the general solution of $\sin^2 x - \cos 2x = 2 - \sin 2x$ is

An aircraft executes a horizontal loop of radius $9 \ km$ at a constant speed of $540 \ km/h$. The wings of the aircraft are banked at an angle of (Acceleration due to gravity $g = 10 \ m/s^2$):

Which one of the following statements is wrong?

The vapour pressure of a solvent decreases by $10 \ mm$ of mercury when a non-volatile solute is added to the solvent. The mole fraction of the solute in the solution is $0.2$. What should be the mole fraction of the solute if the decrease in the vapour pressure is to be $20 \ mm$ of mercury?

Vedclass Test Series

Exam Paper Generator

Online Exam Module