Advertisements
Advertisements
प्रश्न
Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0
Advertisements
उत्तर
3x – 4y + 5 = 0 and 6x – 8y – 15 = 0
The equation of the given lines are
3x – 4y + 5 = 0 ......(1)
6x – 8y – 15 = 0
3x – 4y – 1 = 0 ......(2)
The distance between the parallel lines (1) and (2) is
d = `(5 - ( - 15/2))/sqrt(3^2 + (- 4)^2`
= `(5 + 15/2)/sqrt(9 + 16)`
= `(10 + 15)/(2sqrt(25))`
= `25/(2 xx 5)`
= `5/2`
APPEARS IN
संबंधित प्रश्न
Find the equation of the straight line parallel to 5x − 4y + 3 = 0 and having x-intercept 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 through the point (−1, 2)
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 equation of a straight line parallel to 2x + 3y = 10 and which is such that the sum of its intercepts on the axes is 15
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
Find the distance between the parallel lines
12x + 5y = 7 and 12x + 5y + 7 = 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. Draw graph of the cost as x goes from 0 to 50 copies
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 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:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`
