Question

The set of lines $ax+by+c=0$, where $5a+6b+7c=0$ are concurrent at the point

• A. $(5,6)$
• B. $(\frac{5}{6},\frac{7}{6})$
• C. $(\frac{6}{5},\frac{7}{5})$
• D. $(\frac{5}{7},\frac{6}{7})$

Answer 1

The correct option is D $(\frac{5}{7},\frac{6}{7})$

$ax+by+c=0\Rightarrow \frac{ax}{-c}+\frac{by}{-c}=15a+6b+7=0\Rightarrow \frac{a}{-7/5}+\frac{b}{-7/6}=1$
Hence equation passes through $(\frac{5}{7},\frac{6}{7})$