Question

 

Find the equation to the straight line which passes through the points (3, 4) and having intercepts on the axes: 

1. equal in magnitude but opposite in sign 

2. such that their sum is 14

Solution

Correct option is

x – y + 1 = 0, 4x + 3y = 24 and x + y = 7

 

1. Let intercepts on the axes be a and –a respectively.  

∴ The equation of the line in intercept form is  

           

Since, eq. (i) passes through (3, 4), then   

        3 – 4 = a   

∴     a = –1     

From (i),     

       x – y + 1 = 0    

which is the required equation of the line. 

2. Let the equation of the line be 

This passes through (3, 4) 

Therefore, 

           

It is given that a + b = 14    

∴       b = 14 – a  

Putting b = 14 – in (ii), we get 

        

⇒   42 – 3a + 4a = 14a – a2  

⇒   a2 – 13a + 42 = 0  

⇒   (a – 7)(a – 6) = 0 

∴    a = 6, 7    

Then, 

      b = 8, 7                    (∵ b = 14 – a)  

Hence the required equations are  

      

i.e.,    4x + 3y = 24 and x + y = 7.

SIMILAR QUESTIONS

Q1

Find the equation of a line which makes an angle of 135o with positive direction of x-axis and passes through the point (3, 5).

Q2

Find the equation of the straight line bisecting the segment joining the points (5, 3) and (4, 4) and making an angle of 45o with the positive direction of x-axis.

Q3

Find the equation of the right bisector of the line joining (1, 1) and (3, 5).

Q4

Find the equation to the straight line joining the points .

Q5

 

Let ABC be a triangle with A(–1, –5), B(0, 0) and C(2, 2) and let D be the middle point of BC. Find the equation of the perpendicular drawn from Bto AD.  

 

Q6

The vertices of a triangle are A(10, 4), B(–4, 9) and C(–2, –1). Find the equation of the altitude through A.

Q7

Find the equations of the medians of a triangle, the coordinates of whose vertices are (–1, 6), (–3, –9) and (5, –8).

Q8

Find the ratio in which the line segment joining the points (2, 3) and (4, 5) is divided by the line joining (6, 8) and (–3, –2).

Q9

Find the equation of the line through (2, 3) so that the segment of the line intercepted between the axes is bisected at this point.

Q10

Find the equation of the straight line through the point P(ab) parallel to the lines . Also find the intercepts made by it on the axes.