Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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 perpendicular
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. Draw graph of the cost as x goes from 0 to 50 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
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:
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:
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:
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
