# Find the equation of lines which passes through the point (3,4) and the sum of intercepts on the axes is 14.

## Solution :

Let the equation of line be $$x\over a$$ + $$y\over b$$ = 1  …..(i)

This line passes through (3,4), therefore $$3\over a$$ + $$4\over b$$ = 1  …….(ii)

It is given that a + b = 14  $$\implies$$  b = 14 – a in (ii), we get

$$3\over a$$ + $$4\over 14 – a$$ = 1  $$\implies$$  $$a^2$$ – 13a + 42 = 0

$$\implies$$  (a – 7)(a – 6) = 0  $$\implies$$  a = 7, 6

for a = 7, b = 14 – 7 = 7 and for a = 6, b = 14 – 6 = 8

Putting the values of a and b in (i), we get the equations of lines

$$x\over 7$$ + $$y\over 7$$ = 1  and  $$x\over 6$$ + $$y\over 8$$ = 1

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