Advertisements
Advertisements
Question
Find the equation of a line passing through (3, −2) and perpendicular to the line x − 3y + 5 = 0.
Advertisements
Solution
The equation of the line perpendicular to x − 3y + 5 = 0 is \[3x + y + \lambda = 0\], where
\[\lambda\] is a constant.
It passes through (3, −2).
\[9 - 2 + \lambda = 0\]
\[ \Rightarrow \lambda = - 7\]
Substituting \[\lambda\] = −7 in \[3x + y + \lambda = 0\], we get
\[3x + y - 7 = 0\] , which is the required line.
APPEARS IN
RELATED QUESTIONS
Draw the lines x = − 3, x = 2, y = − 2, y = 3 and write the coordinates of the vertices of the square so formed.
Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x-axis.
Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.
Find the equations to the altitudes of the triangle whose angular points are A (2, −2), B (1, 1) and C (−1, 0).
Find the equation of the straight lines passing through the following pair of point :
(0, −a) and (b, 0)
Find the equation of the straight lines passing through the following pair of point :
(a, b) and (a + b, a − b)
Find the equation of the straight lines passing through the following pair of point :
(a cos α, a sin α) and (a cos β, a sin β)
Find the equations to the diagonals of the rectangle the equations of whose sides are x = a, x = a', y= b and y = b'.
By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.
The vertices of a quadrilateral are A (−2, 6), B (1, 2), C (10, 4), and D (7, 8). Find the equation of its diagonals.
The owner of a milk store finds that he can sell 980 litres milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.
Find the equations to the straight lines which go through the origin and trisect the portion of the straight line 3 x + y = 12 which is intercepted between the axes of coordinates.
Find the equation to the straight line cutting off intercepts 3 and 2 from the axes.
Find the equation to the straight line cutting off intercepts − 5 and 6 from the axes.
Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes
(i) equal in magnitude and both positive,
(ii) equal in magnitude but opposite in sign.
Find the equation to the straight line which cuts off equal positive intercepts on the axes and their product is 25.
Find the equation of the line, which passes through P (1, −7) and meets the axes at A and Brespectively so that 4 AP − 3 BP = 0.
Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
Find the equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on X and Y-axes such that a − b = 2.
Find the equation of the straight line passing through the origin and bisecting the portion of the line ax + by + c = 0 intercepted between the coordinate axes.
The straight line through P (x1, y1) inclined at an angle θ with the x-axis meets the line ax + by + c = 0 in Q. Find the length of PQ.
Find the equation of straight line passing through (−2, −7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.
Find the equation of the line passing through the point of intersection of the lines 4x − 7y − 3 = 0 and 2x − 3y + 1 = 0 that has equal intercepts on the axes.
Three sides AB, BC and CA of a triangle ABC are 5x − 3y + 2 = 0, x − 3y − 2 = 0 and x + y − 6 = 0 respectively. Find the equation of the altitude through the vertex A.
Find the equation of a line passing through the point (2, 3) and parallel to the line 3x − 4y + 5 = 0.
The line 2x + 3y = 12 meets the x-axis at A and y-axis at B. The line through (5, 5) perpendicular to AB meets the x-axis and the line AB at C and E respectively. If O is the origin of coordinates, find the area of figure OCEB.
Find the equation of the straight lines passing through the origin and making an angle of 45° with the straight line \[\sqrt{3}x + y = 11\].
Find the equations to the straight lines which pass through the origin and are inclined at an angle of 75° to the straight line \[x + y + \sqrt{3}\left( y - x \right) = a\].
The equation of the base of an equilateral triangle is x + y = 2 and its vertex is (2, −1). Find the length and equations of its sides.
Prove that the family of lines represented by x (1 + λ) + y (2 − λ) + 5 = 0, λ being arbitrary, pass through a fixed point. Also, find the fixed point.
Find the equation of the straight line which passes through the point of intersection of the lines 3x − y = 5 and x + 3y = 1 and makes equal and positive intercepts on the axes.
The inclination of the straight line passing through the point (−3, 6) and the mid-point of the line joining the point (4, −5) and (−2, 9) is
In what direction should a line be drawn through the point (1, 2) so that its point of intersection with the line x + y = 4 is at a distance `sqrt(6)/3` from the given point.
If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ______.
Equation of the line passing through the point (a cos3θ, a sin3θ) and perpendicular to the line x sec θ + y cosec θ = a is x cos θ – y sin θ = a sin 2θ.
The equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0 is equidistant from the points (0, 0) and (8, 34).
