A straight line parallel to the line y=sqrt{3 | vedclass

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

Question

(C) The slope of the line $y=\sqrt{3}x$ is $m=\sqrt{3}$. Since the required line is parallel to this line,its slope is also $\sqrt{3}$.Thus,$	an 	he

Vedclass · Accepted Answer

$2\sqrt{3}-1$

Vedclass · Answer

(C) The slope of the line $y=\sqrt{3}x$ is $m=\sqrt{3}$. Since the required line is parallel to this line,its slope is also $\sqrt{3}$.Thus,$	an 	heta = \sqrt{3}$,which implies $	heta = 60^{\circ}$.Let the distance $PQ = r$. The coordinates of any point $P$ on the line passing through $Q(2,3)$ at a distance $r$ are given by $(2+r \cos 60^{\circ}, 3+r \sin 60^{\circ}) = (2+\frac{r}{2}, 3+\frac{r\sqrt{3}}{2})$.Since $P$ lies on the line $2x+4y-27=0$,we substitute these coordinates into the equation:$2(2+\frac{r}{2}) + 4(3+\frac{r\sqrt{3}}{2}) - 27 = 0$$4 + r + 12 + 2\sqrt{3}r - 27 = 0$$r(1+2\sqrt{3}) - 11 = 0$$r = \frac{11}{2\sqrt{3}+1}$Rationalizing the denominator:$r = \frac{11(2\sqrt{3}-1)}{(2\sqrt{3}+1)(2\sqrt{3}-1)} = \frac{11(2\sqrt{3}-1)}{12-1} = \frac{11(2\sqrt{3}-1)}{11} = 2\sqrt{3}-1$.Therefore,the length of the line segment $PQ$ is $2\sqrt{3}-1$.

$A$ straight line parallel to the line $y=\sqrt{3}x$ passes through $Q(2,3)$ and cuts the line $2x+4y-27=0$ at $P$. Then the length of the line segment $PQ$ is

Similar Questions

The equation of a line passing through the origin and perpendicular to the line joining $(a, 0)$ and $(-a, 0)$ is

$A$ line $L$ through $A(-5,-4)$ meets the lines $x+3y+2=0$,$2x+y+4=0$,and $x-y-5=0$ at points $B$,$C$,and $D$ respectively. If $\left(\frac{15}{AB}\right)^2+\left(\frac{10}{AC}\right)^2=\left(\frac{6}{AD}\right)^2$,then find the equation of $L$.

The equation of the line passing through the point $(2,3)$ such that its $x$-intercept is twice its $y$-intercept is ......... .

Find the equation of the line passing through the point of intersection of the lines $4x + 7y - 3 = 0$ and $2x - 3y + 1 = 0$ that has equal intercepts on the axes.

Find the equation of the line,which cuts off intercepts on the axes whose sum and product are $1$ and $-6,$ respectively.

Vedclass Test Series

Exam Paper Generator

Online Exam Module