Mathematics

Problem

Which of the following conditions on the ratios

\dfrac{a_1}{a_2},\,\dfrac{b_1}{b_2},\,\dfrac{c_1}{c_2}

guarantees that the two equations

a_1x+b_1y+c_1=0

and

a_2x+b_2y+c_2=0

represent coincident lines? a)

\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}

\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}

\dfrac{a_1}{b_1}=\dfrac{a_2}{b_2}=\dfrac{c_1}{c_2}

\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}