Advertisements
Advertisements
Question
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
Options
9x − 20y + 96 = 0
9x + 20y = 24
20x + 9y + 53 = 0
none of these
Advertisements
Solution
9x − 20y + 96 = 0
Let the required line intersects the coordinate axis at (a, 0) and (0, b).
The point (−4, 3) divides the required line in the ratio 5 : 3
\[\therefore - 4 = \frac{5 \times 0 + 3 \times a}{5 + 3} \text { and } 3 = \frac{5 \times b + 3 \times 0}{5 + 3}\]
\[ \Rightarrow a = \frac{- 32}{3} \text { and } b = \frac{24}{5}\]
Hence, The equation of the required line is given below:
\[\frac{x}{\frac{- 32}{3}} + \frac{y}{\frac{24}{5}} = 1\]
\[ \Rightarrow \frac{- 3x}{32} + \frac{5y}{24} = 1\]
\[ \Rightarrow - 9x + 20y = 96\]
\[ \Rightarrow 9x - 20y + 96 = 0\]
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 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 cos α, a sin α) and (a cos β, a sin β)
Find the equations of the sides of the triangles the coordinates of whose angular point is respectively (0, 1), (2, 0) and (−1, −2).
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.
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 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 line which passes through the point (3, 4) and is such that the portion of it intercepted between the axes is divided by the point in the ratio 2:3.
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 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 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 point (2, 1) and bisecting the portion of the straight line 3x − 5y = 15 lying 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.
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 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 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 of the straight lines passing through (2, −1) and making an angle of 45° with the line 6x + 5y − 8 = 0.
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.
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.
Show that the straight lines given by (2 + k) x + (1 + k) y = 5 + 7k for different values of k pass through a fixed point. Also, find that 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.
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.
If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point
The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 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
Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.
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.
The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line `sqrt(3) x + y` = 1 is ______.
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.
