Which among the following represents the comb | vedclass

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

Question

(A) The given equation is $2x^2 - xy - y^2 = 0$.Factoring the quadratic expression:$2x^2 - 2xy + xy - y^2 = 0$$2x(x - y) + y(x - y) = 0$$(2x + y)(x -

Vedclass · Accepted Answer

$2x^2 - xy - y^2 - 4x + y + 2 = 0$

Vedclass · Answer

(A) The given equation is $2x^2 - xy - y^2 = 0$.Factoring the quadratic expression:$2x^2 - 2xy + xy - y^2 = 0$$2x(x - y) + y(x - y) = 0$$(2x + y)(x - y) = 0$.The lines are parallel to $2x + y = 0$ and $x - y = 0$.Let the required lines be $(2x + y + k_1) = 0$ and $(x - y + k_2) = 0$.Since these lines pass through $(1, 0)$,we substitute the point:For the first line: $2(1) + 0 + k_1 = 0 \Rightarrow k_1 = -2$.For the second line: $1 - 0 + k_2 = 0 \Rightarrow k_2 = -1$.The combined equation is $(2x + y - 2)(x - y - 1) = 0$.Expanding the product:$2x(x - y - 1) + y(x - y - 1) - 2(x - y - 1) = 0$$2x^2 - 2xy - 2x + xy - y^2 - y - 2x + 2y + 2 = 0$$2x^2 - xy - y^2 - 4x + y + 2 = 0$.

Which among the following represents the combined equation of a pair of lines passing through the point $(1, 0)$ and parallel to the lines represented by $2x^2 - xy - y^2 = 0$?

Similar Questions

If one of the lines represented by $ax^2+2hxy+by^2=0$ passes through $(2,3)$ and the other passes through $(4,5)$,then $a+2h+b$ equals

The joint equation of two lines passing through the origin,each making an angle of $30^{\circ}$ with the positive $Y$-axis,is

If $s$ and $p$ are respectively the sum and the product of the slopes of the lines $3x^2 - 2xy - 15y^2 = 0$,then $s:p$ is equal to

The perpendiculars are drawn to lines $L_1$ and $L_2$ from the origin making an angle $\frac{\pi}{4}$ and $\frac{3 \pi}{4}$ respectively with the positive direction of the $X$-axis. If both the lines are at a unit distance from the origin,then their joint equation is

The equation $2x^{2}+5xy-12y^{2}=0$ represents a

Vedclass Test Series

Exam Paper Generator

Online Exam Module