Advertisements
Advertisements
Question
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)
Solution
The equation of the given line is
3x + 4y – 6 = 0 ......(1)
The equation of any line perpendicular to line (1) is
4x – 3y + k = 0 ......(2)
Given that this line is 4 units from the point (2, 1)
∴ 4 = `+- (4(2) - 3(1) + k")/sqrt(4^2 + ( - 3)^2`
± 4 = `(8 - 3 + "k")/sqrt(16 + 9)`
± 4 = `(5 + "k")/5`
5 + k = ± 20
k = ± 20 – 5
k = 20 – 5 or k = -20
k = 15 or k = – 25
∴ The equation of the required lines are
4x – 3y + 15 = 0 and 4x – 3y – 25 = 0
APPEARS IN
RELATED QUESTIONS
Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines
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) perpendicular to 3x + 4y = 6
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 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 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
3x − 4y + 5 = 0 and 6x − 8y − 15 = 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
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
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:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`
