Question

A straight line passes through (2, 3) and the portion of the line intercepted between the axes is bisected at this point. Find its equation

Solution

Correct option is

3x + 2y – 12 = 0

Let the required equation of the line be:

               

The above line meets the X–axis and Y–axis in points (a, 0) and (0, b) respectively

Now the point which bisects the join o f (a, 0) and (b, 0) has coordinates:  

                         

But its given as ≡ (2, 3)   

So on comparing, we get a = 4, b = 6  

Substituting the values of a and b in (i), we get:

                     

or        3x + 2y – 12 = 0 is the required equation. 

SIMILAR QUESTIONS

Q1

Find the incentre of ΔABC if A is (4, –2), B is (–2, 4) and C is (5, 5).

Q2

Find the coordinates of the orthcentre of the triangle whose vertices are (0, 0), (2, –1) and (–1, 3).

Q3

Find straight lines represented by 6x2 + 13xy + 6y2 + 8x + 7y + 2 = 0 and also find the point of intersection.  

Q4

If abc are all distinct, then the equations (b – c)x + (c – a)y + a – b = 0 and (b3 – c3)x + (c3 – a3)y + a3 – b3 = 0 represent the same line if

Q5

If the pair of lines x2 – 2pxy – y2 = 0 and x2 – 2qxy – y2 = 0 are such that each pair bisects the angle between the other pair, then pq equals  

Q6

Angles made with x-axis by the two lines through the point  (1, 2) and cutting the line x + y = 4 at a distance  from the point (1, 2) are

Q7

If the algebraic sum of the perpendicular distances of a variable line from the points (0, 2), (2, 0) and (1, 1) is zero, then the line always passes through the point

Q8

 be three points. Then the equation of the bisector of angle PQR is

Q9

Find the area of triangle ABC with vertices A (aa2), B (bb2), C (cc2).

Q10

Find the slope (m), intercepts on X axis, intercept on Y axis of the line 3x+ 2y – 12 = 0. Also trace the line on XY plane.