English

Determine the Distance Between the Pair of Parallel Lines: Y = Mx + C And Y = Mx + D

Advertisements
Advertisements

Question

Determine the distance between the pair of parallel lines:

y = mx + c and y = mx + d

Short/Brief Note
Advertisements

Solution

 The given parallel lines can be written as
mx − y +c = 0            ... (1)
mx − y +d = 0            ... (2)
Let d be the distance between the given lines.

\[\Rightarrow d = \left| \frac{c - d}{\sqrt{m^2 + 1}} \right|\]

 

shaalaa.com
  Is there an error in this question or solution?
Chapter 23: The straight lines - Exercise 23.16 [Page 114]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 23 The straight lines
Exercise 23.16 | Q 1.3 | Page 114

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).


Find the points on the x-axis, whose distances from the `x/3 +y/4 = 1`  are 4 units.


Find the distance between parallel lines:

15x + 8y – 34 = 0 and 15x + 8y + 31 = 0


Find the distance between parallel lines  l (x + y) + p = 0 and l (x + y) – r = 0


What are the points on the y-axis whose distance from the line  `x/3 + y/4 = 1` is 4 units.


Find perpendicular distance from the origin to the line joining the points (cosΘ, sin Θ) and (cosΦ, sin Φ).


Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x– 7y + 5 = 0 and 3x + y = 0.


A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.


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 direction of x-axis is 15°.


A line passes through a point A (1, 2) and makes an angle of 60° with the x-axis and intersects the line x + y = 6 at the point P. Find AP.


Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to a line having slope 3/4.


Find the distance of the line 2x + y = 3 from the point (−1, −3) in the direction of the line whose slope is 1.


Find the equation of a line perpendicular to the line \[\sqrt{3}x - y + 5 = 0\] and at a distance of 3 units from the origin.


Find the distance of the point (4, 5) from the straight line 3x − 5y + 7 = 0.


Show that the perpendiculars let fall from any point on the straight line 2x + 11y − 5 = 0 upon the two straight lines 24x + 7y = 20 and 4x − 3y − 2 = 0 are equal to each other.


Find the distance of the point of intersection of the lines 2x + 3y = 21 and 3x − 4y + 11 = 0 from the line 8x + 6y + 5 = 0.


What are the points on X-axis whose perpendicular distance from the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] is a ?


Determine the distance between the pair of parallel lines:

8x + 15y − 34 = 0 and 8x + 15y + 31 = 0


Determine the distance between the pair of parallel lines:

4x + 3y − 11 = 0 and 8x + 6y = 15


Find the equations of the lines through the point of intersection of the lines x − y + 1 = 0 and 2x − 3y+ 5 = 0, whose distance from the point(3, 2) is 7/5.


If the centroid of a triangle formed by the points (0, 0), (cos θ, sin θ) and (sin θ, − cos θ) lies on the line y = 2x, then write the value of tan θ.


The line segment joining the points (−3, −4) and (1, −2) is divided by y-axis in the ratio


The value of λ for which the lines 3x + 4y = 5, 5x + 4y = 4 and λx + 4y = 6 meet at a point is


The vertices of a triangle are (6, 0), (0, 6) and (6, 6). The distance between its circumcentre and centroid is


A plane passes through (1, - 2, 1) and is perpendicular to two planes 2x - 2y + z = 0 and x - y + 2z = 4. The distance of the plane from the point (1, 2, 2) is ______.


Show that the locus of the mid-point of the distance between the axes of the variable line x cosα + y sinα = p is `1/x^2 + 1/y^2 = 4/p^2` where p is a constant.


The distance of the point P(1, – 3) from the line 2y – 3x = 4 is ______.


The distance between the lines y = mx + c1 and y = mx + c2 is ______.


The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is ______.


A straight line passes through the origin O meet the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment Q in the ratio:


Find the length of the perpendicular drawn from the point P(3, 2, 1) to the line `overliner = (7hati + 7hatj + 6hatk) + λ(-2hati + 2hatj + 3hatk)`


The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.


The distance between the parallel lines 3x − 4y + 7 = 0 and 3x − 4y + 5 = 0 is `a/b`. Value of a + b is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×