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

Asked by Abhisek | 11 months ago |  77

1 Answer

Solution :-

We know that equation of the line making intercepts a and b on x-and y-axis, respectively, is 

\( \dfrac{x}{a}+\dfrac{y}{b}=1 \) . … (1)

Given: sum of intercepts = 9

a + b = 9

b = 9 – a

Now, substitute value of b in the above equation, we get

\( \dfrac{x}{a}+\dfrac{y}{9-a}=1 \)

Given: the line passes through the point (2, 2),

So, \( \dfrac{2}{a}+\dfrac{2}{9-a}=1 \)

\( \dfrac{(2(9 – a) + 2a)}{a(9 – a)}=1\)

\( \dfrac{(18 – 2a + 2a)}{a(9 – a)}\) = 1

\( \dfrac{18}{a(9 – a)}\) = 1

18 = a (9 – a)

18 = 9a – a2

a2 – 9a + 18 = 0

Upon factorizing, we get

a2 – 3a – 6a + 18 = 0

a (a – 3) – 6 (a – 3) = 0

(a – 3) (a – 6) = 0

a = 3 or a = 6

Let us substitute in (1),

Case 1 (a = 3):

Then b = 9 – 3 = 6

\( \dfrac{x}{3}+\dfrac{y}{6}=1\)

2x + y = 6

2x + y – 6 = 0

Case 2 (a = 6):

Then b = 9 – 6 = 3

\( \dfrac{x}{6}+\dfrac{y}{3}=1\)

x + 2y = 6

x + 2y – 6 = 0

The equation of the line is 2x + y – 6 = 0 or x + 2y – 6 = 0.

Answered by Pragya Singh | 11 months ago

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