A) \[|6\alpha +2\beta |=19\]
B) \[|2\alpha +6\beta |=11\]
C) \[|6\alpha +2\beta |=9\]
D) \[|2\alpha +6\beta |=19\]
Correct Answer: A
Solution :
\[{{\left. \frac{dy}{dx} \right|}_{\left( \alpha ,\beta \right)}}=\frac{-{{\alpha }^{2}}-3}{{{\left( {{\alpha }^{2}}-3 \right)}^{2}}}\] Given that : \[\frac{-{{\alpha }^{2}}-3}{{{\left( {{\alpha }^{2}}-3 \right)}^{2}}}=-\frac{1}{3}\]\[\Rightarrow \alpha =0,\pm 3\]\[(\alpha \ne 0)\] \[\Rightarrow \beta =\pm \frac{1}{2}.\] \[(\beta \ne 0)\] \[|6\alpha +2\beta |=19\]
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