A point on the parabola $y^2=18 x$ at which the ordinate increases at twice the rate of the abscissa is

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Aicharya · Accepted Answer

Any point be $\left(\frac{9}{2} t^2, 9 tight) ;$ differentiating $y^2=18 x$ $ \begin{aligned} & \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{9}{\mathrm{y}}=\frac{1}{\mathrm{t}}=2 	ext { (given) } \Rightarrow \mathrm{t}=\frac{1}{2} . \ & \Rightarrow 	ext { Point is }\left(\frac{9}{8}, \frac{9}{2}ight) \end{aligned} $

A point on the parabola $y^2=18 x$ at which the ordinate increases at twice the rate of the abscissa is

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