Q. 275.0( 1 Vote )

# 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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