English

Find the Equation to the Straight Line Cutting off Intercepts 3 and 2 from the Axes.

Advertisements
Advertisements

Question

Find the equation to the straight line cutting off intercepts 3 and 2 from the axes.

Answer in Brief
Advertisements

Solution

Here, a = 3, b = 2
So, the equation of the line is

\[\frac{x}{a} + \frac{y}{b} = 1\]

\[ \Rightarrow \frac{x}{3} + \frac{y}{2} = 1\]

\[ \Rightarrow 2x + 3y - 6 = 0\]

shaalaa.com
Equations of Line in Different Forms - Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
  Is there an error in this question or solution?
Chapter 23: The straight lines - Exercise 23.6 [Page 46]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 23 The straight lines
Exercise 23.6 | Q 1.1 | Page 46

RELATED QUESTIONS

Find the equation of the line parallel to x-axis and passing through (3, −5).


Find the equation of the line parallel to x-axis and having intercept − 2 on 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 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.


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 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 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 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.


A line is such that its segment between the straight lines 5x − y − 4 = 0 and 3x + 4y − 4 = 0 is bisected at the point (1, 5). Obtain its equation.


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 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 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 to the straight lines passing through the point (2, 3) and inclined at and angle of 45° to the line 3x + y − 5 = 0.


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.


Find the equation of the straight line passing through the point of intersection of 2x + y − 1 = 0 and x + 3y − 2 = 0 and making with the coordinate axes a triangle of area \[\frac{3}{8}\] sq. units.


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 area of the triangle formed by the coordinate axes and the line (sec θ − tan θ) x + (sec θ + tan θ) y = 2.


If the diagonals of the quadrilateral formed by the lines l1x + m1y + n1 = 0, l2x + m2y + n2 = 0, l1x + m1y + n1' = 0 and l2x + m2y + n2' = 0 are perpendicular, then write the value of l12 − l22 + m12 − m22.


If a, b, c are in G.P. write the area of the triangle formed by the line ax + by + c = 0 with the coordinates axes.


A line passes through the point (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is


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


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 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).


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×