Advertisements
Advertisements
प्रश्न
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.
उत्तर
We have,
4x − 7y − 3 = 0 ... (1)
2x − 3y + 1 = 0 ... (2)
Solving (1) and (2) using cross-multiplication method:
\[\frac{x}{- 7 - 9} = \frac{y}{- 6 - 4} = \frac{1}{- 12 + 14}\]
\[ \Rightarrow x = - 8, y = - 5\]
Thus, the point of intersection of the given lines is \[\left( - 8, - 5 \right)\].
\[\therefore \frac{- 8}{a} - \frac{5}{a} = 1\]
\[ \Rightarrow - 8 - 5 = a\]
\[ \Rightarrow a = - 13\]
Hence, the equation of the required line is \[\frac{x}{- 13} + \frac{y}{- 13} = 1 \text { or } x + y + 13 = 0 .\]
APPEARS IN
संबंधित प्रश्न
Find the equation of the line parallel to x-axis and passing through (3, −5).
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 passing through (−2, 3) and inclined at an angle of 45° with the x-axis.
Find the equation of the line passing through \[(2, 2\sqrt{3})\] and inclined with x-axis at an angle of 75°.
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 \[\frac{3}{5}\].
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 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, 0) and (2, −2)
Find the equation of the straight lines passing through the following pair of point :
(a, b) and (a + c sin α, b + c cos α)
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.
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 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.
A straight line passes through the point (α, β) and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is \[\frac{x}{2 \alpha} + \frac{y}{2 \beta} = 1\].
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.
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.
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 the straight line perpendicular to 5x − 2y = 8 and which passes through the mid-point of the line segment joining (2, 3) and (4, 5).
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.
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 length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a cos α, a sin α) and (a cos β, a sin β).
Find the equations to the straight lines which pass through the point (h, k) and are inclined at angle tan−1 m to the straight line y = mx + c.
The equation of one side of an equilateral triangle is x − y = 0 and one vertex is \[(2 + \sqrt{3}, 5)\]. Prove that a second side is \[y + (2 - \sqrt{3}) x = 6\] and find the equation of the third side.
Find the equations of the two straight lines through (1, 2) forming two sides of a square of which 4x+ 7y = 12 is one diagonal.
Two sides of an isosceles triangle are given by the equations 7x − y + 3 = 0 and x + y − 3 = 0 and its third side passes through the point (1, −10). Determine the equation of the third side.
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.
Write the integral values of m for which the x-coordinate of the point of intersection of the lines y = mx + 1 and 3x + 4y = 9 is an integer.
The equation of the straight line which passes through the point (−4, 3) such that the portion of the line between the axes is divided internally by the point in the ratio 5 : 3 is
If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point
A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.
Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is `7/5`
