Advertisements
Advertisements
Question
Find the distance between the parallel lines
12x + 5y = 7 and 12x + 5y + 7 = 0
Solution
2x + 5y = 7 and 12x + 5y + 7 = 0
The equation of the given lines are
12x + 5y – 7 = 0 ......(1)
12x + 5y + 7 = 0 .......(2)
The distance between the parallel lines
ax + by + c1 = 0 and ax + by + c2 = 0 is
The equation of any line parallel to (1) is
d = `("c"_1 + "c"_2)/sqrt("a"^2 + "b"^2)`
∴ The required distance - `(- 7 - 7)/sqrt(12^2 + 5^2)`
= `(-14)/sqrt(144 + 25)`
= `- 14/sqrt(169)`
= `- 14/13`
The distance cannot be negative
∴ Required distance = `14/13`
APPEARS IN
RELATED QUESTIONS
Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines
Find the distance between the line 4x + 3y + 4 = 0, and a point (−2, 4)
Write the equation of the lines through the point (1, −1) parallel to x + 3y − 4 = 0
Write the equation of the lines through the point (1, −1) perpendicular to 3x + 4y = 6
Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and through the point (−1, 2)
Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and parallel to x − y + 5 = 0
Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0
Find the family of straight lines perpendicular
Find the family of straight lines parallel to 3x + 4y – 12
A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq.units
A photocopy store charges ₹ 1.50 per copy for the first 10 copies and ₹ 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying. Find the cost of making 40 copies
Find all the equations of the straight lines in the family of the lines y = mx − 3, for which m and the x-coordinate of the point of intersection of the lines with x − y = 6 are integers
Choose the correct alternative:
The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are
Choose the correct alternative:
The equation of the line with slope 2 and the length of the perpendicular from the origin equal to `sqrt(5)` is
Choose the correct alternative:
The point on the line 2x − 3y = 5 is equidistance from (1, 2) and (3, 4) is
Choose the correct alternative:
If the two straight lines x + (2k − 7)y + 3 = 0 and 3kx + 9y − 5 = 0 are perpendicular then the value of k is
Choose the correct alternative:
If a vertex of a square is at the origin and its one side lies along the line 4x + 3y − 20 = 0, then the area of the square is
Choose the correct alternative:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`
