The equation of the straight line cutting off | vedclass

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

Question

(D) The equation of a line in slope-intercept form is given by $y = mx + c$.Given that the line is inclined at $30^\circ$ to the positive direction of

Vedclass · Accepted Answer

$\sqrt{3}y - x + 2\sqrt{3} = 0$

Vedclass · Answer

(D) The equation of a line in slope-intercept form is given by $y = mx + c$.Given that the line is inclined at $30^\circ$ to the positive direction of the $x$-axis,the slope $m = 	an(30^\circ) = \frac{1}{\sqrt{3}}$.The line cuts off an intercept of $2$ from the negative direction of the $y$-axis,so $c = -2$.Substituting these values into the equation,we get $y = \frac{1}{\sqrt{3}}x - 2$.Multiplying both sides by $\sqrt{3}$,we get $\sqrt{3}y = x - 2\sqrt{3}$.Rearranging the terms,we obtain $\sqrt{3}y - x + 2\sqrt{3} = 0$.

The equation of the straight line cutting off an intercept of $2$ from the negative direction of the $y$-axis and inclined at $30^\circ$ to the positive direction of the $x$-axis is:

Similar Questions

The equations of the sides $AB$,$AC$,and $BC$ of a $\triangle ABC$ are respectively $x-3y=0$,$3x-y=0$,and $x+y+4=0$. If $P$ and $Q$ are points on the line $3x-y+k=0$ passing through $B$ such that $PB:BQ=1:1$,then $k=$

$A$ line $L$ passes through the point $P(1, 2)$ and makes an angle of $60^{\circ}$ with the positive $X$-axis. $A$ and $B$ are two points lying on $L$ at a distance of $4$ units from $P$. If $O$ is the origin,then the area of $\triangle OAB$ is

Find the equation of the line passing through the point $(0, 2)$ making an angle of $\frac{2 \pi}{3}$ with the positive $x$-axis. Also,find the equation of the line parallel to it and crossing the $y$-axis at a distance of $2$ units below the origin.

Find the equation of a line perpendicular to the line $x-2y+3=0$ and passing through the point $(1, -2).$

Find the equation of the line passing through the point $(3, 4)$ and making intercepts on the axes of equal magnitude but opposite signs.

Vedclass Test Series

Exam Paper Generator

Online Exam Module