Advertisements
Advertisements
प्रश्न
Find the distance between the parallel lines
12x + 5y = 7 and 12x + 5y + 7 = 0
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the equation of the straight line parallel to 5x − 4y + 3 = 0 and having x-intercept 3
Find the distance between the line 4x + 3y + 4 = 0, and a point (−2, 4)
Find the distance between the line 4x + 3y + 4 = 0, and a point (7, −3)
Write the equation of the lines through the point (1, −1) parallel to x + 3y − 4 = 0
Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and perpendicular to x − 2y + 1 = 0
Find the equations of straight lines which are perpendicular to the line 3x + 4y − 6 = 0 and are at a distance of 4 units from (2, 1)
Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from (−10, −2) to the line x + y − 2 = 0
If p1 and p2 are the lengths of the perpendiculars from the origin to the straight lines x sec θ + y cosec θ = 2a and x cos θ – y sin θ = a cos 2θ, then prove that p12 + p22 = a2
Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0
Find the family of straight lines perpendicular
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
Find the image of the point (−2, 3) about the line x + 2y − 9 = 0
Find atleast two equations of the straight lines in the family of the lines y = 5x + b, for which b and the x-coordinate of the point of intersection of the lines with 3x − 4y = 6 are integers
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:
A line perpendicular to the line 5x − y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq.units, then its equation is
Choose the correct alternative:
If the lines represented by the equation 6x2 + 41xy – 7y2 = 0 make angles α and β with x-axis then tan α tan β =
