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Question -

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.



Answer -

The equation of a line in the intercept form is
 
Here, a and b are the intercepts on x and y axes respectively.
It is given that a + b = 9 ⇒ b = 9 – a … (ii)
From equations (i) and (ii), we obtain
 
It is given that the line passes through point (2, 2). Therefore, equation (iii) reduces to
 
If a = 6 and b = 9 – 6 = 3, then the equation of the line is
 
If a = 3 and b = 9 – 3 = 6, then the equation of the line is

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