CBSE - Class 11 Mathematics Straight Lines Worksheet
Miscellaneous Exercise on Chapter 9
1.
If the lines $y = 3x +1$ and $2y = x + 3$ are equally inclined to the line $y = mx + 4$, find the value of $m$.
2.
Find the value of $p$ so that the three lines $3x + y – 2 = 0$, $px + 2 y – 3 = 0$ and $2x – y – 3 = 0$ may intersect at one point.
3.
Find the image of the point (3, 8) with respect to the line $x +3y = 7$ assuming the line to be a plane mirror.
4.
Find the equation of a line drawn perpendicular to the line $\frac{x}{4} + \frac{y}{6} = 1$ through the point, where it meets the y-axis.
5.
Find equation of the line which is equidistant from parallel lines $9x + 6y – 7 = 0$ and $3x + 2y + 6 = 0$.
6.
If sum of the perpendicular distances of a variable point P ($x$, $y$) from the lines $x + y – 5 = 0$ and $3x – 2y +7 = 0$ is always 10. Show that P must move on a line.
7.
Find the area of the triangle formed by the lines $y – x = 0$, $x + y = 0$ and $x – k = 0$.
8.
In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line $x + y = 4$?
9.
What are the points on the y-axis whose distance from the line $\frac{x}{3} + \frac{y}{4} = 1$ is 4 units.
10.
Find perpendicular distance from the origin to the line joining the points (cos$\theta$, sin$\theta$) and (cos$\phi$, sin$\phi$).
11.
Find the values of $k$ for which the line $(k–3) x – (4 – k^2) y + k^2 –7k + 6 = 0$ is (c) Passing through the origin.
12.
Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line $x + y = 4$ may be at a distance of 3 units from this point.
13.
Find the distance of the line $4x + 7y + 5 = 0$ from the point (1, 2) along the line $2x – y = 0$.
14.
Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively.
15.
A person standing at the junction (crossing) of two straight paths represented by the equations $2x – 3y + 4 = 0$ and $3x + 4y – 5 = 0$ wants to reach the path whose equation is $6x – 7y + 8 = 0$ in the least time. Find equation of the path that he should follow.
16.
Find the values of $k$ for which the line $(k–3) x – (4 – k^2) y + k^2 –7k + 6 = 0$ is (a) Parallel to the x-axis,
17.
The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle which are parallel to the axes.
18.
Prove that the product of the lengths of the perpendiculars drawn from the points ($\sqrt{a^2 - b^2}, 0$) and ($-\sqrt{a^2 - b^2}, 0$) to the line $\frac{x}{a} \cos\theta + \frac{y}{b} \sin\theta = 1$ is $b^2$.
19.
Find the equation of the lines through the point (3, 2) which make an angle of $45^\circ$ with the line $x – 2y = 3$.
20.
If three lines whose equations are $y = m_1x + c_1$, $y = m_2x + c_2$ and $y = m_3x + c_3$ are concurrent, then show that $m_1(c_2 – c_3) + m_2(c_3 – c_1) + m_3(c_1 – c_2) = 0$.
