A) \[\left( -\frac{9}{8},\frac{9}{2} \right)\]
B) \[(2,-4)\]
C) \[(2,4)\]
D) \[\left( \frac{9}{8},\frac{9}{2} \right)\]
Correct Answer: D
Solution :
Given curve is\[{{y}^{2}}=18x\] \[\therefore \] \[2y\frac{dy}{dt}=18\frac{dx}{dt}\] \[\Rightarrow \] \[2y\left( 2\frac{dx}{dt} \right)=18\frac{dx}{dt}\] \[\left( \because \frac{dy}{dt}=2\frac{dx}{dt}given \right)\] \[\Rightarrow \] \[y=\frac{9}{2}\] \[\therefore \] \[x=\frac{{{y}^{2}}}{18}=\frac{81}{4\times 18}=\frac{9}{8}\]
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