Advertisements
Advertisements
Question
Determine the distance between the pair of parallel lines:
y = mx + c and y = mx + d
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.
APPEARS IN
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 distance between parallel lines:
15x + 8y – 34 = 0 and 15x + 8y + 31 = 0
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 co-ordinates of the point, which divides the line segment joining the points A(2, − 6, 8) and B(− 1, 3, − 4) externally in the ratio 1 : 3.
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 distance of the point (2, 3) from the line 2x − 3y + 9 = 0 measured along a line making an angle of 45° with the x-axis.
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.
The perpendicular distance of a line from the origin is 5 units and its slope is − 1. Find the equation of the line.
Find the perpendicular distance from the origin of the perpendicular from the point (1, 2) upon the straight line \[x - \sqrt{3}y + 4 = 0 .\]
What are the points on y-axis whose distance from the line \[\frac{x}{3} + \frac{y}{4} = 1\] is 4 units?
Show that the path of a moving point such that its distances from two lines 3x − 2y = 5 and 3x + 2y = 5 are equal is a straight line.
If the length of the perpendicular from the point (1, 1) to the line ax − by + c = 0 be unity, show that \[\frac{1}{c} + \frac{1}{a} - \frac{1}{b} = \frac{c}{2ab}\] .
Determine the distance between the pair of parallel lines:
4x − 3y − 9 = 0 and 4x − 3y − 24 = 0
Find 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
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.
The distance between the orthocentre and circumcentre of the triangle with vertices (1, 2), (2, 1) and \[\left( \frac{3 + \sqrt{3}}{2}, \frac{3 + \sqrt{3}}{2} \right)\] is
Area of the triangle formed by the points \[\left( (a + 3)(a + 4), a + 3 \right), \left( (a + 2)(a + 3), (a + 2) \right) \text { and } \left( (a + 1)(a + 2), (a + 1) \right)\]
The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.
Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 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
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 the tangent to the curve y = 3x2 - 2x + 1 at a point Pis parallel toy = 4x + 3, the co-ordinates of P are
Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.
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 of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is ______.
A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 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 ______.
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:
The distance of the point (2, – 3, 1) from the line `(x + 1)/2 = (y - 3)/3 = (z + 1)/-1` is ______.
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
