Advertisements
Advertisements
प्रश्न
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)
Advertisements
उत्तर
The equation of the straight line passing through the point of intersection of the lines.
4x – y + 3 = 0 and 5x + 2y + 7 = 0 is
(4x – y + 3) + λ(5x + 2y + 7) = 0 ......(1)
Through the point (–1, 2)
Given that line (1) passes through the point (–1, 2)
(1) ⇒ (4(–1) – 2 + 3) + λ(5(–1) + 2(2) + 7) = 0
(– 4 – 2 + 3) + λ(– 5 + 4 + 7) = 0
– 3 + 6λ = 0
⇒ λ = `3/6 = 1/2`
∴ The equation of the required line is
`(4x - y + 3) + 1/2 (5x + 2y + 7)` = 0
2(4x – y + 3) + (5x + 2y + 7) = 0
8x – 2y + 6 + 5x + 2y + 7 = 0
13x +13 = 0
⇒ x + 1 = 0
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 (7, −3)
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
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 perpendicular to x − 2y + 1 = 0
Find the equations of two straight lines which are parallel to the line 12x + 5y + 2 = 0 and at a unit distance from the point (1, −1)
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 family of straight lines perpendicular
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
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. 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 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:
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
