Class 11 Straight Lines Exemplar 9 2 Exemplar Solutions

Q1

Find the equation of the line which passes through the point $(2, 2\sqrt{3})$ and makes an angle of $75^\circ$ with the positive direction of the $x$-axis.

Q2

Find the equation of the line passing through $(-3, 5)$ and perpendicular to the line through $(2, 5)$ and $(-3, 6)$.

Q3

Find the coordinates of the foot of the perpendicular from the point $(-1, 3)$ to the line $3x - 4y - 16 = 0$.

Q4

Find the value of $k$ so that the line $2x + ky - 9 = 0$ may be perpendicular to the line $3x - 4y + 7 = 0$.

Q5

Find the distance of the line $4x - y = 0$ from the point $P(4, 1)$ measured along the line making an angle of $135^\circ$ with the positive direction of the $x$-axis.

Q6

Find the equation of the line whose perpendicular distance from the origin is $4$ units and the angle which the normal makes with the positive $x$-axis is $15^\circ$.

Q7

If the lines $ax + 2y + 1 = 0$, $bx + 3y + 1 = 0$ and $cx + 4y + 1 = 0$ are concurrent, prove that $a, b, c$ are in A.P.

Q8

Find the equation of the line passing through the intersection of $2x + 3y - 4 = 0$ and $x - 5y = 7$ that has $x$-intercept equal to $-4$.

Q9

Find the acute angle between the lines $y - \sqrt{3}x - 5 = 0$ and $\sqrt{3}y - x + 6 = 0$.

Q10

Find the value of $p$ so that the three lines $3x + y - 2 = 0$, $px + 2y - 3 = 0$ and $2x - y - 3 = 0$ may intersect at one point.

Q11

If the intercept of a line between the coordinate axes is divided by the point $(-5, 4)$ in the ratio $1 : 2$, find the equation of the line.

Q12

Find the distance between the parallel lines $15x + 8y - 34 = 0$ and $15x + 8y + 31 = 0$.

Q13

Find the area of the triangle formed by the line $x\cos\alpha + y\sin\alpha = p$ with the coordinate axes.

Q14

Find the coordinates of the image of the point $(1, 2)$ with respect to the line $x - 3y + 4 = 0$.

Q15

A line is such that its segment between the lines $5x - y + 4 = 0$ and $3x + 4y - 4 = 0$ is bisected at the point $(1, 5)$. Obtain its equation.

Chapter 9 - Straight Lines

Overview

Short Answer Type Questions