Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
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
If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal
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 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 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
Find the image of the point (−2, 3) about the line x + 2y − 9 = 0
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 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 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
