Advertisements
Advertisements
Question
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
Advertisements
Solution
The equation of the given line is
2x + 3y = 10 ......(1)
The equation of any line parallel to (1) is
2x + 3y = k ......(2)
`(2x)/"k" + (3y)/"k"` = 1
`x/("k"/2) + y/("k"/3)` = 1
Given that the sum of the intercepts of the line (2) on the axes is 15
∴ `"k"/2 + "k"/3` = 15
`(3"k" + 2k")/6` = 15
5k = 90
⇒ k = `90/5`
= 18
∴ The equation of the required line is 2x + 3y = 18
APPEARS IN
RELATED QUESTIONS
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 parallel to x − y + 5 = 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 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
12x + 5y = 7 and 12x + 5y + 7 = 0
Find the family of straight lines parallel to 3x + 4y – 12
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then find the equation of the line in new position
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and it passes through the point (5, 3). Find the co-ordinates of the point A
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 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 slope of the line which makes an angle 45° with the line 3x − y = −5 are
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 point on the line 2x − 3y = 5 is equidistance from (1, 2) and (3, 4) is
Choose the correct alternative:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`
