A) \[(2,\,4)\]
B) \[(2,\,-4)\]
C) \[\left( -\frac{9}{8},\frac{9}{2} \right)\]
D) \[\left( \frac{9}{8},\frac{9}{2} \right)\]
Correct Answer: D
Solution :
Equation of parabola is\[{{y}^{2}}=18x\]. Differentiate w.r. to t, we get \[2y\frac{dy}{dt}=18\frac{dx}{dt}\] \[2.2y=18\] \[\left( \because \frac{dy}{dt}=2\frac{dx}{dt} \right)\] \[y=\frac{9}{2}\] \[\therefore \]From equation of parabola \[{{\left( \frac{9}{2} \right)}^{2}}=18x\] \[\Rightarrow \] \[\frac{81}{4}=18x\Rightarrow x=\frac{81}{4\times 18}\] \[\Rightarrow \] \[x=\frac{9}{8}\] \[\therefore \] Point is\[\left( \frac{9}{8},\frac{9}{2} \right)\].
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