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

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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 – a 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.

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