A straight line passing through the origin O | vedclass

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

Question

(B) Let the equation of the line passing through the origin be $y = mx$. The given parallel lines are $L_1: 4x + 2y - 9 = 0$ and $L_2: 2x + y + 6 = 0$

Vedclass · Accepted Answer

$3 : 4$

Vedclass · Answer

(B) Let the equation of the line passing through the origin be $y = mx$. The given parallel lines are $L_1: 4x + 2y - 9 = 0$ and $L_2: 2x + y + 6 = 0$. Note that $L_1$ can be written as $2(2x + y) = 9$,or $2x + y = 4.5$. Let the line $y = mx$ intersect $L_1$ at $P(x_1, y_1)$ and $L_2$ at $Q(x_2, y_2)$. For point $P$: $2x_1 + y_1 = 4.5$ and $y_1 = mx_1$. Substituting $y_1$,we get $x_1(2 + m) = 4.5$,so $x_1 = \frac{4.5}{2 + m}$. For point $Q$: $2x_2 + y_2 = -6$ and $y_2 = mx_2$. Substituting $y_2$,we get $x_2(2 + m) = -6$,so $x_2 = \frac{-6}{2 + m}$. Since $O(0,0)$ divides $PQ$ in ratio $k:1$,we have $0 = \frac{k x_2 + 1 x_1}{k + 1}$. This implies $k x_2 + x_1 = 0$,or $k = -\frac{x_1}{x_2}$. Substituting the values: $k = -\frac{4.5 / (2 + m)}{-6 / (2 + m)} = \frac{4.5}{6} = \frac{4.5}{6} = \frac{9}{12} = \frac{3}{4}$. Thus,the ratio is $3:4$.

$A$ straight line passing through the origin $O$ meets the parallel lines $4x + 2y = 9$ and $2x + y + 6 = 0$ at points $P$ and $Q$ respectively. In what ratio does the point $O$ divide the line segment $PQ$?

Similar Questions

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ and $l^2 = m^2 + n^2$ is

The magnetic flux through a circuit of resistance $R$ changes by an amount $\Delta \phi$ in time $\Delta t$. Then the total quantity of electric charge $Q$ passing during this time through any point of the circuit is given by:

Which of the following alkali metal ions has the lowest ionic mobility in an aqueous solution?

Which of the following elements does not show variable valency?

If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it,then (both $x$ and $h$ being much smaller than the radius of the earth)

Vedclass Test Series

Exam Paper Generator

Online Exam Module