Question

For what values of a and b the intercepts cut off on the coordinate axes by the line $a x + b y + 8 = 0$ are equal in length but opposite in signs to those cut off by the line $2 x - 3 y + 6 = 0$ 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: (D)

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

Answer 2

The equation of lines in intercept form are

$\frac { x } { - 8 / a } + \frac { y } { - 8 / b } = 1$ .....(i)

$\frac { x } { - 3 } + \frac { y } { 2 } = 1$ .....(ii)

According to the condition,

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

$\Rightarrow a = - \frac { 8 } { 3 }$ and $- \frac { 8 } { b } = - ( 2 ) \Rightarrow b = 4$.