Question

Find the equation of line(s) which passes through the point $(22,-6)$ and whose intercept on the x-axis exceeds the intercept on y-axis by 5

• A. $11x+6y-66=0$ or $10x+5y-10=0$
• B. $6x-11y+66=0$ or $2x-y+10=0$
• C. $6x+11y-66=0$ or $x+2y-10=0$
• D. None of these

Answer 1

The correct option is C $6x+11y-66=0$ or $x+2y-10=0$

Let equation of line be $\frac{x}{a}+\frac{y}{b}=1$

Here $y-$ intercept is $b$

$x-$ intercept is $a$

Also again $a=b+5$

So $\frac{x}{b+5}+\frac{y}{b}=1$, it pass through $(22,-6)$

$\frac{22}{b+5}-\frac{6}{b}=1\Rightarrow 22b-b(b+5)=6(b+5)$

$\Rightarrow b^2+5b=22b-6b-30$

$\Rightarrow b^2+5b=16b-30$

$\Rightarrow b^2-11b+30=0\Rightarrow (b-5)(b-6)=0$

$b=5,6$

so $a=10$ for $b=5$

$a=11$ for $b=6$

equation of lines are $\frac{x}{10}+\frac{y}{5}=1$

$\frac{x}{11}+\frac{y}{6}=1$

$x+2y=10$ and $6x+11y=66$

$x+2y-10$ and $6x+11y-66=0$.