A) \[\left( \frac{9}{8},\frac{9}{2} \right)\]
B) (2, ? 4)
C) \[\left( \frac{-9}{8},\frac{9}{2} \right)\]
D) (2, 4)
Correct Answer: A
Solution :
\[{{y}^{2}}=18x\] Differentiate both sides w.r.t. t \[2y\left( \frac{dy}{dt} \right)=18\left( \frac{dx}{dt} \right)\] Þ \[2y\left( 2\frac{dx}{dt} \right)=18\left( \frac{dx}{dt} \right)\],\[\left( \because \frac{dy}{dt}=2\frac{dx}{dt} \right)\] \ \[4y=18\] or \[y=\frac{9}{2}\] and \[x=\frac{{{y}^{2}}}{18}=\frac{9}{8}\] Hence the required point is \[\left( \frac{9}{8},\frac{9}{2} \right)\].
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