Advertisements
Advertisements
प्रश्न
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.
उत्तर
The x - coordinate of the point A is given by
\[- 4 = \frac{3 \times a + 5 \times 0}{3 + 5}\]
\[ \Rightarrow a = \frac{- 32}{3}\]
The y - coordinate of the point B is given by
\[3 = \frac{3 \times 0 + 5 \times b}{3 + 5}\]
\[ \Rightarrow b = \frac{24}{5}\]
The equation of the line passing is given by
\[\frac{x}{\frac{- 32}{3}} + \frac{y}{\frac{24}{5}} = 1\]
\[ \Rightarrow 9x - 20y + 96 = 0\]
APPEARS IN
संबंधित प्रश्न
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 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 passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.
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 :
(at1, a/t1) and (at2, a/t2)
Find the equations of the sides of the triangles the coordinates of whose angular point is respectively (0, 1), (2, 0) and (−1, −2).
Find the equations of the medians of a triangle, the coordinates of whose vertices are (−1, 6), (−3, −9) and (5, −8).
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 of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
Find the equation of the straight line which passes through the point P (2, 6) and cuts the coordinate axes at the point A and B respectively so that \[\frac{AP}{BP} = \frac{2}{3}\] .
Find the equation of the straight line passing through the point (2, 1) and bisecting the portion of the straight line 3x − 5y = 15 lying between 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 the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 .
Find the equation of a line passing through (3, −2) and perpendicular to the line x − 3y + 5 = 0.
Find the equation of the straight line through the point (α, β) and perpendicular to the line lx + my + n = 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 length of the perpendicular from the point (4, −7) to the line joining the origin and the point of intersection of the lines 2x − 3y + 14 = 0 and 5x + 4y − 7 = 0.
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 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.
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.
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.
Find the equation of the straight line drawn through the point of intersection of the lines x + y = 4 and 2x − 3y = 1 and perpendicular to the line cutting off intercepts 5, 6 on the axes.
Write the equation of the line passing through the point (1, −2) and cutting off equal intercepts from the axes.
If the point (5, 2) bisects the intercept of a line between the axes, then its equation is
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.
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.
If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ______.
The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.
