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 - a²) = 1

⇒ 18//(9a - a²) = 1

⇒ 18 = 9a - a²

⇒ a² - 9a + 18 = 0

⇒ a² - 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

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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