The equations of the lines passing through th | vedclass

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

Question

(A) Let $m_1$ be the slope of the line passing through $(3,2)$ and $m_2$ be the slope of $x-2y=3$. $m_2 = \frac{-1}{-2} = \frac{1}{2}$. The angle betw

Vedclass · Accepted Answer

$3x-y=7$ and $x+3y=9$

Vedclass · Answer

(A) Let $m_1$ be the slope of the line passing through $(3,2)$ and $m_2$ be the slope of $x-2y=3$. $m_2 = \frac{-1}{-2} = \frac{1}{2}$. The angle between the lines is $45^{\circ}$,so $	an 45^{\circ} = \left| \frac{m_1 - m_2}{1 + m_1 m_2} ight|$. $1 = \left| \frac{m_1 - 1/2}{1 + m_1/2} ight| = \left| \frac{2m_1 - 1}{2 + m_1} ight|$. Case $1$: $\frac{2m_1 - 1}{2 + m_1} = 1$ $\Rightarrow 2m_1 - 1 = 2 + m_1$ $\Rightarrow m_1 = 3$. The equation is $y - 2 = 3(x - 3)$ $\Rightarrow y - 2 = 3x - 9$ $\Rightarrow 3x - y = 7$. Case $2$: $\frac{2m_1 - 1}{2 + m_1} = -1$ $\Rightarrow 2m_1 - 1 = -2 - m_1$ $\Rightarrow 3m_1 = -1$ $\Rightarrow m_1 = -1/3$. The equation is $y - 2 = -\frac{1}{3}(x - 3)$ $\Rightarrow 3y - 6 = -x + 3$ $\Rightarrow x + 3y = 9$. Thus,the equations are $3x - y = 7$ and $x + 3y = 9$.

The equations of the lines passing through the point $(3,2)$ which make an angle of $45^{\circ}$ with the line $x-2y=3$ are

Similar Questions

Consider the straight lines:
$L_1 : x - y = 1$
$L_2 : x + y = 1$
$L_3 : 2x + 2y = 5$
$L_4 : 2x - 2y = 7$
The correct statement is:

Show that the equation of the line passing through the origin and making an angle $\theta$ with the line $y=mx+c$ is $\frac{y}{x}=\frac{m \pm \tan \theta}{1 \mp m \tan \theta}$.

If the equation of a line having a slope $m$ $(m \in \mathbb{Z})$,passing through $(1, 1)$ and making an angle of $\tan^{-1}\left(\frac{5}{7}\right)$ with the line $x + y - 3 = 0$ is $ax + y + c = 0$,then $ac =$

Find the acute angle between the lines $y = 3$ and $y = \sqrt{3}x + 9$. (in $^{\circ}$)

Find the equation of the lines passing through the origin and making an angle of $\tan^{-1} m$ with the line $y = mx + c$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module