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Question
Find the point on the curve y2 = 8x for which the abscissa and ordinate change at the same rate ?
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Solution
\[\text { Here }, \]
\[ y^2 = 8x . . . \left( 1 \right)\]
\[\Rightarrow2y\frac{dy}{dt}=8\frac{dx}{dt}\]
\[\Rightarrow2y=8\left[ \because \frac{dy}{dt}=\frac{dx}{dt} \right]\]
\[\Rightarrow y =4\]
\[\Rightarrow x=\frac{y^2}{8}\left[ \text { From eq }.\left( 1 \right) \right]\]
\[\Rightarrow x=\frac{16}{8}=2\]
\[\text { So, the point is }\left( 2, 4 \right).\]
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