Q27 of 51 Page 10

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


Let the intercepts on the axes be a and b

Therefore, a + b = 9 ⇒ b = 9 – a

Now, equation of the line in intercept form is

= 1

or = 1

(2, 2) lies on it.

⇒ = 1

or = 1

or 18 = a(9 – a)

or 18 = 9a – a2

or a2 – 9a + 18 = 0

⇒(a – 6)(a – 3) = 0

Hence a = 3, 6

Case (i), When a = 3 ∴ b = 6

Equation of the line is

= 1

2x + y = 6 (Required line)

Case (ii), when a = 6, ∴ b = 3

Equation of the line is

= 1

x + 2y = 6 (Required equation)

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