Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9
Concept Used:
The equation of the line with intercepts a and b is
Given:
Here, a+b = 9
Explanation:
⇒ b = 9 – a ……(i)
The line is passing through (2, 2).
……(ii)
From equation (i) and (ii)
⇒18 – 2a + 2a = 9a – a2
⇒a2 – 9a +18 = 0
⇒ (a – 3)(a – 6) = 0
⇒a = 3, 6
For a = 3, b = 9 – 3 = 6
For a = 6, b = 9 – 6 = 3
Thus the equation of line is
or
⇒2x + y = 6 or x + 2y = 6
Hence, the equation of line is 2x + y = 6 or x + 2y = 6