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

If the lines `(x-1)/2=(y+1)/3=(z-1)/4 ` and `(x-3)/1=(y-k)/2=z/1` intersect each other then find value of k


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  l (x + y) + p = 0 and l (x + y) – r = 0


Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.


Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle tan−1 \[\left( \frac{5}{12} \right)\] with the positive direction of x-axi .


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 (3, 5) from the line 2x + 3y = 14 measured parallel to a line having slope 1/2.


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 point (3, 5) from the line 2x + 3y = 14 measured parallel to the line x − 2y = 1.


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


Find the perpendicular distance of the line joining the points (cos θ, sin θ) and (cos ϕ, sin ϕ) from the origin.


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 ?


What are the points on y-axis whose distance from the line \[\frac{x}{3} + \frac{y}{4} = 1\]  is 4 units?

 

If sum of perpendicular distances of a variable point P (xy) from the lines x + y − 5 = 0 and 3x − 2y + 7 = 0 is always 10. Show that P must move on a line.


Determine the distance between the pair of parallel lines:

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


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.


Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is


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


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


The shortest distance between the lines

`bar"r" = (hat"i" + 2hat"j" + hat"k") + lambda (hat"i" - hat"j" + hat"k")` and

`bar"r" = (2hat"i" - hat"j" - hat"k") + mu(2hat"i" + hat"j" + 2hat"k")` is


If P(α, β) be a point on the line 3x + y = 0 such that the point P and the point Q(1, 1) lie on either side of the line 3x = 4y + 8, then _______.


Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.


Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.


The distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is ______.


A point moves so that square of its distance from the point (3, –2) is numerically equal to its distance from the line 5x – 12y = 3. The equation of its locus is ______.


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 point of intersection of the diagonals of the rectangle whose sides are contained in the lines x = 8, x = 10, y = 11, and y =12 is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×