The value(s) of \( a \) for which two curves \( y=a x^{2}+a x+\frac...

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The value(s) of \( a \) for which two curves \( y=a x^{2}+a x+\frac{1}{24} \)
\( \mathrm{P} \) and \( x=a y^{2}+a y+\frac{1}{24} \) touch each other is/are

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(1) \( \frac{2}{3} \)
(2) \( \frac{1}{3} \)
(3) \( \frac{3}{2} \)
(4) \( \frac{1}{2} \)
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