Question

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

Answer 1

$\text{Equation of line in intercept form is}\frac{x}{a}+\frac{y}{b}=1...\left(i\right)Given,a+b=9...\left(ii\right)\text{And line (i) passes through the piont (2, 2) i.e., it will satisfy the line (i)i.e., put}x=2,y=2inEq.\left(i\right)\Rightarrow \frac{2}{a}+\frac{2}{b}=1...\left(iii\right)\text{Solve, Eqs, (ii) and (iii), to find the values of a and b.}\text{From Eq. (ii), b = 9 - a put in Eq. (iii), we get}\frac{2}{a}+\frac{2}{9-a}=1\Rightarrow 2(9-a)+2a=a(9-a)\Rightarrow 18-2a+2a=9a-a^2\Rightarrow a^2-9a+18=0\text{Factorize it by splitting the middle term,}\Rightarrow a^2-6a-3a+18=0\Rightarrow a(a-6)-3(a-6)=0\Rightarrow (a-6)(a-3)=0\Rightarrow a=6or3\Rightarrow b=3or6\text{Hence, Eq. (i) becomes}\frac{x}{6}+\frac{y}{3}=1or\frac{x}{3}+\frac{y}{6}=1\Rightarrow 3x+6y=18or6x+3y=18\Rightarrow x+2y=6or2x+y=6$