| Assertion (A): \[\text{3x}+\text{4y}+\text{5}=0\] and \[\text{6x}+k\text{y}+\text{9}=0\]represent parallel lines if \[k=8.\] |
| Reason (R): \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]represent parallel lines if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\]. |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: A
Solution :
| [a] In assertion, given lines represent parallel lines, if |
| \[\frac{3}{6}=\frac{4}{k}\ne \frac{5}{9}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k=\frac{6\times 4}{3}=8\] |
| Reason is also true. |
| Also, reason is the correct explanation for assertion. |
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