Advertisements
Advertisements
Question
Find the joint equation of the line passing through (-1, 2) and perpendicular to the lines x + 2y + 3 = 0 and 3x - 4y - 5 = 0
Advertisements
Solution
Let L1 and L2 be the lines passing through the origin and perpendicular to the lines x + 2y + 3 = 0 and 3x - 4y - 5 = 0 respectively.
Slopes of the lines x + 2y + 3 = 0 and 3x - 4y - 5 = 0 are `-1/2` and `- 3/-4 = 3/4` respectively.
∴ slopes of the lines L1 and L2 are `2` and `(-4)/3` respectively.
Since the lines L1 and L2 pass through the point (-1, 2), their equations are
∴ (y - y1) = m(x - x1)
∴ (y - 2)= 2(x + 1)
⇒ y - 2 = 2x + 2
⇒ 2x - y + 4 = 0 and
∴ (y - 2) = `((-4)/3)`(x + 1)
⇒ 3y - 6 = (- 4)(x + 1)
⇒ 3y - 6 = - 4x - 4
⇒ 4x + 3y - 6 + 4 = 0
⇒ 4x + 3y - 2 = 0
their combined equation is
∴ (2x - y + 4)(4x + 3y - 2) = 0
∴ 8x2 + 6xy - 4x - 4xy - 3y2 + 2y + 16x + 12y - 8 = 0
∴ 8x2 + 2xy + 12x - 3y2 + 14y - 8 = 0
APPEARS IN
RELATED QUESTIONS
Find the combined equation of the following pair of lines:
2x + y = 0 and 3x − y = 0
Find the combined equation of the following pair of lines passing through point (2, 3) and parallel to the coordinate axes.
Find the separate equation of the line represented by the following equation:
3y2 + 7xy = 0
Find the separate equation of the line represented by the following equation:
5x2 – 9y2 = 0
Find the separate equation of the line represented by the following equation:
`3"x"^2 - 2sqrt3"xy" - 3"y"^2 = 0`
Find the separate equation of the line represented by the following equation:
x2 + 2(cosec α)xy + y2 = 0
Find the separate equation of the line represented by the following equation:
x2 + 2xy tan α - y2 = 0
Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by following equation:
5x2 - 8xy + 3y2 = 0
Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:
5x2 + 2xy - 3y2 = 0
Choose correct alternatives:
If two lines ax2 + 2hxy + by2 = 0 make angles α and β with X-axis, then tan (α + β) = _____.
Choose correct alternatives:
If the equation 3x2 – 8xy + qy2 + 2x + 14y + p = 1 represents a pair of perpendicular lines, then the values of p and q are respectively ______.
Choose correct alternatives:
If h2 = ab, then slopes of lines ax2 + 2hxy + by2 = 0 are in the ratio
Choose correct alternatives:
If distance between lines (x - 2y)2 + k(x - 2y) = 0 is 3 units, then k = ______.
Find the joint equation of the line passing through the origin and having inclinations 60° and 120°.
Find the joint equation of the line passing through (1, 2) and parallel to the coordinate axes
Show that the following equations represents a pair of line:
x2 + 2xy - y2 = 0
Show that the following equations represents a pair of line:
4x2 + 4xy + y2 = 0
Show that the following equations represent a pair of line:
`"x"^2 - 2sqrt3"xy" - "y"^2 = 0`
Find the separate equation of the line represented by the following equation:
6x2 - 5xy - 6y2 = 0
Find the separate equation of the line represented by the following equation:
x2 - 4y2 = 0
Find the separate equation of the line represented by the following equation:
3x2 - y2 = 0
Find the separate equation of the line represented by the following equation:
2x2 + 2xy - y2 = 0
Find k, if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.
Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0.
If the line 4x - 5y = 0 coincides with one of the lines given by ax2 + 2hxy + by2 = 0, then show that 25a + 40h + 16b = 0
Show that the following equation represents a pair of line. Find the acute angle between them:
2x2 + xy - y2 + x + 4y - 3 = 0
Find k if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.
Find the joint equation of the line passing through the origin and having slopes 1 + `sqrt3` and 1 - `sqrt3`
The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis is ______
Show that the combined equation of pair of lines passing through the origin is a homogeneous equation of degree 2 in x and y. Hence find the combined equation of the lines 2x + 3y = 0 and x − 2y = 0
The joint equation of pair of lines through the origin, each of which makes an angle of 60° with Y-axis, is ______
The joint equation of the lines through the origin which forms two of the sides of the equilateral triangle having x = 2 as the third side is ______
The equation of line passing through the midpoint of the line joining the points (-1, 3, -2) and (-5, 3, -6) and equally inclined to the axes is ______.
The combined equation of the lines which pass through the origin and each of which makes an angle of 30° with the line 3x + 2y – 11 = 0 is ______.
Write the separate equations of lines represented by the equation 5x2 – 9y2 = 0
Write the joint equation of co-ordinate axes.
Find the combined equation of the pair of lines passing through the origin and perpendicular to the lines represented by 3x2 + 2xy – y2 = 0.
If `x^2/a + y^2/b + (2xy)/h` = 0 represents a pair of lines and slope of one line is twice the other, then find the value of ab : h2.
Find the joint equation of the pair of lines through the origin and perpendicular to the lines given by 2x2 + 7xy + 3y2 = 0
The distance between the lines represented by the equation 4x² + 4xy + y² − 6x − 3y − 4 = 0 is
