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

Q : 13         Find equation of the line passing through the point  (2,2) and cutting off intercepts on the axes whose sum is 9.
 

Answers (1)

best_answer

Let (a, b) are the intercept on x and y axis respectively
Then, the equation of line is given by
\frac{x}{a}+\frac{y}{b}= 1
It is given that
a + b = 9 
b = 9 - a
Now,
\frac{x}{a}+\frac{y}{9-a } = 1\\ \\ x(9-a)+ay= a(9-a)\\ 9x-ax+ay=9a-a^2
It is given that line passes through point (2 ,2)
So,
9(2)-2a+2a=9a-a^2\\ a^2-9a+18=0\\ a^2-6a-3a+18=0\\ (a-6)(a-3)= 0\\ a=6 \ \ \ \ \ \ or \ \ \ \ \ \ a = 3

case (i)  a = 6  b = 3
 \frac{x}{6}+\frac{y}{3}= 1\\ \\ x+2y = 6

case (ii)   a = 3 , b = 6
\frac{x}{3}+\frac{y}{6}= 1\\ \\ 2x+y = 6
Therefore, equation of line is 2x + y = 6 , x + 2y = 6

Posted by

Gautam harsolia

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