If the equation of a line having a slope m (m | vedclass

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

Question

(B) The slope of the line is $m$. The slope of the line $x + y - 3 = 0$ is $m_2 = -1$. Given $	an 	heta = \left|\frac{m - m_2}{1 + m m_2}ight| = \

Vedclass · Accepted Answer

$-42$

Vedclass · Answer

(B) The slope of the line is $m$. The slope of the line $x + y - 3 = 0$ is $m_2 = -1$. Given $	an 	heta = \left|\frac{m - m_2}{1 + m m_2}ight| = \frac{5}{7}$. Substituting $m_2 = -1$,we get $\left|\frac{m + 1}{1 - m}ight| = \frac{5}{7}$. This implies $7|m + 1| = 5|1 - m|$. Case $1$: $7(m + 1) = 5(1 - m)$ $\Rightarrow 7m + 7 = 5 - 5m$ $\Rightarrow 12m = -2$ $\Rightarrow m = -1/6$. Case $2$: $7(m + 1) = -5(1 - m)$ $\Rightarrow 7m + 7 = -5 + 5m$ $\Rightarrow 2m = -12$ $\Rightarrow m = -6$. Since $m \in \mathbb{Z}$,we must have $m = -6$. The equation of the line passing through $(1, 1)$ with slope $m = -6$ is $y - 1 = -6(x - 1)$. $y - 1 = -6x + 6 \Rightarrow 6x + y - 7 = 0$. Comparing with $ax + y + c = 0$,we get $a = 6$ and $c = -7$. Therefore,$ac = 6 	imes (-7) = -42$.

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 $ac =$

Similar Questions

The equation of a straight line passing through the point $(1, 2)$ and inclined at $45^{\circ}$ to the line $y = 2x + 1$ is

If the line segment joining the points $(5, 2)$ and $(2, a)$ subtends an angle $\frac{\pi}{4}$ at the origin,then the absolute value of the product of all possible values of $a$ is:

Show that two lines $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,where $b_{1}, b_{2} \neq 0$,are perpendicular if $a_{1}a_{2} + b_{1}b_{2} = 0$.

If the coordinates of the vertices $A, B, C$ of the triangle $ABC$ are $(-4, 2)$,$(12, -2)$,and $(8, 6)$ respectively,then $\angle B$ =

If $S_1$ and $S_2$ are two straight lines such that the reflection of $S_1$ in $S_2$ and the reflection of $S_2$ in $S_1$ coincide,the angle between $S_1$ and $S_2$ is equal to?

Vedclass Test Series

Exam Paper Generator

Online Exam Module