The equation of a line which makes an angle o | vedclass

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

Question

(A) The given pair of lines is $xy-x-y+1=0$. Factorizing the equation: $x(y-1)-1(y-1)=0$,which gives $(x-1)(y-1)=0$. Thus,the lines are $x=1$ (a verti

Vedclass · Accepted Answer

$x-y=5$

Vedclass · Answer

(A) The given pair of lines is $xy-x-y+1=0$. Factorizing the equation: $x(y-1)-1(y-1)=0$,which gives $(x-1)(y-1)=0$. Thus,the lines are $x=1$ (a vertical line) and $y=1$ (a horizontal line). Let the required line be $y=mx+c$. The angle between the line $y=mx+c$ and $y=1$ (slope $m_1=0$) is $45^{\circ}$. Using $	an 	heta = |\frac{m-m_1}{1+mm_1}|$,we get $	an 45^{\circ} = |\frac{m-0}{1+0}| = 1$,so $m=1$ or $m=-1$. If $m=1$,the line is $y=x+c$,or $x-y+c'=0$. Checking the options,$x-y=5$ (or $x-y-5=0$) is a line with slope $m=1$. This line makes an angle of $45^{\circ}$ with both $x=1$ and $y=1$.

The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $xy-x-y+1=0$ is

Similar Questions

$A$ block of weight $W$ is held against a vertical wall by applying a horizontal force $F$. The minimum value of $F$ needed to hold the block is

The more commonly used baking powder contains about $30 \% NaHCO_3$,$20 \% NaAl(SO_4)_2$,$10 \% Ca(H_2PO_4)_2$ and $40 \% \text{starch}$. Which of the following statements is/are correct?

Find the derivative of the function: $(x+\cos x)(x-\tan x)$

The sensitivity of a galvanometer is $60 \text{ div/A}$. When a shunt is used,its sensitivity becomes $10 \text{ div/A}$. If the resistance of the galvanometer is $20 \ \Omega$,then the value of the shunt used is: (in $\Omega$)

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20 \ cm$ and $40 \ cm$ and carry $0.2 \ A$ and $0.3 \ A$ current respectively in opposite directions. The magnetic induction (in $T$) at the centre is

Vedclass Test Series

Exam Paper Generator

Online Exam Module