Question

If the line $ax+by+c=0;a\ne 0,b\ne 0$ is perpendicular to line $3y+4x+5=0$, then the value of $\frac{3}{a}+\frac{4}{b}$ is

• A. $5$
• B. $\frac{1}{3}$
• C. $1$
• D. $0$

Answer 1

The correct option is D $0$

$ax+by+c=0$
Slope of the line $m_1=-\frac{a}{b}$
$3y+4x+5=0$
Slope of the line $m_2=-\frac{4}{3}$
If both the lines are perpendicular then,
$m_1\times m_2=-1\Rightarrow -\frac{a}{b}\times -\frac{4}{3}=-1\Rightarrow \frac{a}{b}=-\frac{3}{4}\Rightarrow \frac{4}{b}=-\frac{3}{a}\Rightarrow \frac{3}{a}+\frac{4}{b}=0$