Question

For what value of $a$ and $b$ the intercepts cut on the co-ordinate axes by the line $ax-by+8=0$ are equal in length but opposite in signs to those cut off by the line $2x-3y+6=0$ on the axes.

• A. $a=\frac{8}{3},b=-4$
• B. $a=-\frac{8}{3,}b=-4$
• C. $a=-\frac{8}{3},b=4$
• D. $a=\frac{8}{3},b=4$

Answer 1

Answer: (B)

$a=-\frac{8}{3,}b=-4$

$2x-3y+6=0$

The $x$ intercept of this line is $(-3,0)$

and $y$ intercept of the line is $(0,2)$

$ax-by+8=0$

The $x$ intercept of this line is $(\frac{-8}{a},0)$

and $y$ intercept of the line is $(0,\frac{8}{b})$

The intercepts are opposite is sign;

$-(-3)=\frac{-8}{a}$ and $-2=\frac{8}{b}$

$a=\frac{-8}{3}$ and $b=-4$