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 $(x-3)(y+4)=0$. This represents the lines $x=3$ and $y=-4$.The second pair of lines is

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 $(x-3)(y+4)=0$. This represents the lines $x=3$ and $y=-4$.The second pair of lines is $xy-3x+4y-12=0$,which factors as $(x+4)(y-3)=0$. This represents the lines $x=-4$ 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 $(x-y)(x+y+1) = 0$,which is $x^2-y^2+x-y=0$.

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

$\int\left(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}\right) d x$ is equal to

For a suitably chosen real constant $a$,let a function $f: R - \{-a\} \rightarrow R$ be defined by $f(x) = \frac{a-x}{a+x}$. Further,suppose that for any real number $x \neq -a$ and $f(x) \neq -a$,$(f \circ f)(x) = x$. Then $f\left(\frac{-1}{2}\right)$ is equal to

Which of the following factors are favourable for the formation of oxyhaemoglobin in alveoli?

Which of the following statements about the Bohr model of the hydrogen atom is false?

If $(1, 3), (2, 5),$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module