Advertisements
Advertisements
प्रश्न
Find the equation of the straight lines passing through the following pair of point :
(0, 0) and (2, −2)
Advertisements
उत्तर
0, 0) and (2, −2)
\[\text { Here, } \left( x_1 , y_1 \right) \equiv \left( 0, 0 \right) \]
\[\left( x_2 , y_2 \right) \equiv \left( 2, - 2 \right)\]
So, the equation of the line passing through the two points (0, 0) and (2, −2) is
\[y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}\left( x - x_1 \right)\]
\[ \Rightarrow y - 0 = \frac{- 2 - 0}{2 - 0}\left( x - 0 \right)\]
\[ \Rightarrow y = - x\]
APPEARS IN
संबंधित प्रश्न
Find the equation of the line perpendicular to x-axis and having intercept − 2 on x-axis.
Find the equation of the line parallel to x-axis and having intercept − 2 on y-axis.
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 a line equidistant from the lines y = 10 and y = − 2.
Find the equation of the straight line which passes through the point (1,2) and makes such an angle with the positive direction of x-axis whose sine is \[\frac{3}{5}\].
Find the equation of the straight line passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.
Prove that the perpendicular drawn from the point (4, 1) on the join of (2, −1) and (6, 5) divides it in the ratio 5 : 8.
Find the equation of the line passing through the point (−3, 5) and perpendicular to the line joining (2, 5) and (−3, 6).
Find the equation of the straight lines passing through the following pair of point :
(0, −a) and (b, 0)
By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.
Find the equation to the straight line which bisects the distance between the points (a, b), (a', b') and also bisects the distance between the points (−a, b) and (a', −b').
Find the equation to the straight line cutting off intercepts − 5 and 6 from the axes.
Find the equation of the straight line which passes through (1, −2) and cuts off equal intercepts on 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 of the line which passes through the point (− 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.
Find the equation of the straight line which passes through the point (−3, 8) and cuts off positive intercepts on the coordinate axes whose sum is 7.
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 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 equations of the straight lines which pass through the origin and trisect the portion of the straight line 2x + 3y = 6 which is intercepted between the axes.
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.
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.
If the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] passes through the point of intersection of the lines x + y = 3 and 2x − 3y = 1 and is parallel to x − y − 6 = 0, find a and b.
Find the equation of the line passing through the intersection of the lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
Find the equation of a line passing through (3, −2) and perpendicular to the line x − 3y + 5 = 0.
Find the equation of a line drawn perpendicular to the line \[\frac{x}{4} + \frac{y}{6} = 1\] through the point where it meets the y-axis.
Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x − 3y = 7.
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 \[x + y + \sqrt{3}\left( y - x \right) = a\].
Find the equations of two straight lines passing through (1, 2) and making an angle of 60° with the line x + y = 0. Find also the area of the triangle formed by the three lines.
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.
Find the equations of the lines through the point of intersection of the lines x − 3y + 1 = 0 and 2x + 5y − 9 = 0 and whose distance from the origin is \[\sqrt{5}\].
Write the area of the triangle formed by the coordinate axes and the line (sec θ − tan θ) x + (sec θ + tan θ) y = 2.
Write the equation of the line passing through the point (1, −2) and cutting off equal intercepts from the axes.
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.
The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is ______.
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).
