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 parallel to x − y + 5 = 0
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)
Equation of a line parallel to x – y + 5 = 0 will be of the form x – y + k = 0.
It passes through (–1, –1)
⇒ – 1 + 1 + k = 0
⇒ k = 0.
So the required line is x – y = 0 ⇒ x = y.
APPEARS IN
संबंधित प्रश्न
Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines
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) 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 through the point (−1, 2)
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 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 image of the point (−2, 3) about the line x + 2y − 9 = 0
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 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 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
Choose the correct alternative:
If the lines represented by the equation 6x2 + 41xy – 7y2 = 0 make angles α and β with x-axis then tan α tan β =
Choose the correct alternative:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`
