Question

Find the equation of the straight line passing through the point $(2,2)$ and the sum of the intercepts is $9$.

• A. $2x+y-6=0$, $x+2y-6=0$
• B. $2x+y+6=0$, $x+2y-6=0$
• C. $2x+y-4=0$, $x+2y-6=0$
• D. None of these

Answer 1

The correct option is A $2x+y-6=0$, $x+2y-6=0$

Let $a,b$ the intercepts.

Given that $a+b=9----\left(1\right)$

We know that equation of a line in the intercept form is $\frac{x}{a}+\frac{y}{b}=1$.

Given that the required line is passing through the point $(2,2)$.

$\frac{2}{a}+\frac{2}{b}=1$

$2(a+b)=ab$

$2\left(9\right)=ab$

$ab=18$

$a=\frac{18}{b}---\left(2\right)$

Substitute the value of $a$ in $\left(1\right)$, we get

$\frac{18}{b}+b=9$

$18+b^2=9b$

$b^2-9b+18=0$

$b^2-6b-3b-18=0$

$b(b-6)-3(b-6)=0$

$b=3$ or $b=6$

Substitute b value in (2), we get

$a=6$ or $a=3$

The required equation is

$(a,b)=(6,3)$

$\frac{x}{6}+\frac{y}{3}=1$

$x+2y=6\Rightarrow x+2y-6=0$

Or

$(a,b)=(3,6)$

$\frac{x}{3}+\frac{y}{6}=1$

$2x+y=6\Rightarrow 2x+y-6=0$

Hence, this is the answer.