\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] |
\[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] |
A) If \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}},\] then the line will be coincident
B) If \[\frac{{{a}_{1}}}{{{a}_{2}}}\]and \[\frac{{{b}_{1}}}{{{b}_{2}}}\] are not equal, then the line will be intersecting
C) If \[\frac{{{a}_{1}}}{{{a}_{2}}}\]and \[\frac{{{b}_{1}}}{{{b}_{2}}}\] are equal, then the line will be intersecting
D) If \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}},\] then the lines will be parallel
E) None of these
Correct Answer: C
Solution :
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