Question

The straight line $ax+by+c=0(a,b,c\ne 0)$ will pass through the first quadrant if

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

Answer 1

Answer: (D)

$ac<0$ and/or $bc<0$

A line can pass through the first quadrant if
a) $X$ and $Y$ intercept are positive
b) Only $X$ intercept is positive
c) Only $Y$ intercept is positive
$X$intercept$=\frac{-c}{a}=\frac{-c^2}{ac}$
$Y$intercept$=\frac{-c}{b}=\frac{-c^2}{bc}$
For case -a ) $ac<0$ , and $bc<0$
For case - b ) $ac<0$ , and $bc>0$
For case - c ) $ac>0$ and $bc<0$
Hence, the common intersection is $ac<0$ or $bc<0$ or both $ac<0$ and $bc<0$
Hence, Option D is correct.