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# Find the equation of the line passing through the points (2, 2) and cutting off intercepts on the axis whose sum is 9

**Solution:**

The equation of a line in the intercept form is

x/a + y/b = 1 ....(1)

Here, a and b are the x-intercept and the y-intercept respectively

It is given that

a + b = 9

b = 9 - a ....(2)

From equation (1) and (2), we obtain

x/a + y/(9 - a) = 1 ....(3)

It is given that the line passes through point (2, 2).

Therefore, equation (3) reduces to

⇒ 2/a + 2/(9 - a) = 1

⇒ 2(9 - a)/a(9 - a) + 2a = 1

⇒ (18 - 2a + 2a)/(9a - a^{2}) = 1

⇒ 18//(9a - a^{2}) = 1

⇒ 18 = 9a - a^{2}

⇒ a^{2} - 9a + 18 = 0

⇒ a^{2} - 6a - 3a + 18 = 0

⇒ a(a - 6) - 3(a - 6) = 0

⇒ (a - 6)(a - 3) = 0

⇒ a = 6 or a = 3

- If a = 6 then b = 9 - 6 = 3,

Hence, the equation of the line is

⇒ x/6 + y/3 = 1

⇒ x + 2y - 6 = 0

- If a = 3 then b = 9 - 3 = 6

Hence, the equation of the line is

⇒ x/3 + y/6 = 1

⇒ 2x + y - 6 = 0

Thus, the equation of the line is x + 2y - 6 = 0 or 2x + y - 6 = 0

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 13

## Find the equation of the line passing through the points (2, 2) and cutting off intercepts on the axis whose sum is 9

**Summary:**

The equation of the line passing through the points (2, 2) and cutting off intercepts on the axis whose sum is 9 is x + 2y - 6 = 0 or 2x + y - 6 = 0

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