Question

The straight line $ax+by+c=0$ where $abc\ne$ 0 will pass through the first quadrant if

• A. $ac>0,bc>0$
• B. $c>0$ and $bc<0$
• C. $bc>0$ and/or $ac>0$
• D. $ac<0$ and/or $bc<0$

Answer 1

The correct option is D $ac<0$ and/or $bc<0$

Intercept form of a straight line is $\frac{x}{a}+\frac{y}{b}=1$ here $a$ and $b$ are respectively intercepts on $x$ and $y$ axis
Converting the given equation into intercept form we get $\frac{x}{\frac{-a}{c}}+\frac{y}{\frac{-b}{c}}=1$
therefore the line intersects $x-$axis at $(-\frac{c}{a},0)$ and $y-$axis at $(0,-\frac{c}{b})$
for the line to be in first quadrant $\frac{-c}{a}>0$ and $\frac{-c}{b}>0$
Multiplying both sides of inequality by $a^2$ and $b^2$ respectively we get $ac<0$ and $bc<0$