The combined equation of the diagonals of the | vedclass

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

Question

(D) The first pair of lines is $xy+4x-3y-12=0$,which factors as $(x-3)(y+4)=0$. Thus,the lines are $x=3$ and $y=-4$.The second pair of lines is $xy-3x

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The first pair of lines is $xy+4x-3y-12=0$,which factors as $(x-3)(y+4)=0$. Thus,the lines are $x=3$ and $y=-4$.The second pair of lines is $xy-3x+4y-12=0$,which factors as $(x+4)(y-3)=0$. Thus,the lines are $x=-4$ and $y=3$.The four lines forming the square are $x=3, x=-4, y=-4, y=3$.The vertices of the square are $(3, 3), (3, -4), (-4, -4), (-4, 3)$.The diagonals connect $(3, 3)$ to $(-4, -4)$ and $(3, -4)$ to $(-4, 3)$.The equation of the diagonal passing through $(3, 3)$ and $(-4, -4)$ is $y-3 = \frac{-4-3}{-4-3}(x-3)$,which simplifies to $y-3 = x-3$,or $x-y=0$.The equation of the diagonal passing through $(3, -4)$ and $(-4, 3)$ is $y-(-4) = \frac{3-(-4)}{-4-3}(x-3)$,which simplifies to $y+4 = -1(x-3)$,or $x+y+1=0$.The combined equation is $(x-y)(x+y+1) = x^2+xy+x-xy-y^2-y = x^2-y^2+x-y=0$.

The combined equation of the diagonals of the square formed by the two pairs of straight lines given by $xy+4x-3y-12=0$ and $xy-3x+4y-12=0$ is

Similar Questions

If the equations of the opposite sides of a parallelogram are $x^2 - 7x + 6 = 0$ and $y^2 - 14y + 40 = 0$,then the equation of one of its diagonals is

The pair of straight lines $x^2 - 4xy + y^2 = 0$ together with the line $x + y + 4 = 0$ form a triangle which is:

The pairs of straight lines $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a

If the equation of the pair of lines passing through $(1, 1)$ and perpendicular to the pair of lines $2x^2 + xy - y^2 - x + 2y - 1 = 0$ is $ax^2 + 2hxy + by^2 + 2gx + 3y = 0$,then $\frac{b}{a} =$

The orthocentre of the triangle formed by the lines $x+3y=10$ and $6x^2+xy-y^2=0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module