हिंदी

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

Advertisements
Advertisements

प्रश्न

Determine the distance between the pair of parallel lines:

y = mx + c and y = mx + d

टिप्पणी लिखिए
Advertisements

उत्तर

 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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 23: The straight lines - Exercise 23.16 [पृष्ठ ११४]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 23 The straight lines
Exercise 23.16 | Q 1.3 | पृष्ठ ११४

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


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


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.


Prove that the line y − x + 2 = 0 divides the join of points (3, −1) and (8, 9) in the ratio 2 : 3.


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 a drawn through A (4, −1) parallel to the line 3x − 4y + 1 = 0. Find the coordinates of the two points on this line which are at a distance of 5 units from A.


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


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.


Find the perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line \[x - \sqrt{3}y + 4 = 0 .\]


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:

4x + 3y − 11 = 0 and 8x + 6y = 15


Find the equation of two straight lines which are parallel to + 7y + 2 = 0 and at unit distance from the point (1, −1).

Answer 3:


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


Write the value of θ ϵ \[\left( 0, \frac{\pi}{2} \right)\] for which area of the triangle formed by points O (0, 0), A (a cos θ, b sin θ) and B (a cos θ, − b sin θ) is maximum.


If the lines x + ay + a = 0, bx + y + b = 0 and cx + cy + 1 = 0 are concurrent, then write the value of 2abc − ab − bc − ca.


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


The area of a triangle with vertices at (−4, −1), (1, 2) and (4, −3) is


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


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.


If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point.


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


A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is ______.


The value of the λ, if the lines (2x + 3y + 4) + λ (6x – y + 12) = 0 are

Column C1 Column C2
(a) Parallel to y-axis is (i) λ = `-3/4`
(b) Perpendicular to 7x + y – 4 = 0 is (ii) λ = `-1/3`
(c) Passes through (1, 2) is (iii) λ = `-17/41`
(d) Parallel to x axis is λ = 3

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


The distance of the point (-3, 2, 3) from the line passing through (4, 6, -2) and having direction ratios -1, 2, 3 is ______units.


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


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×