The point on the curve $y^{2} = 8 x$ for which the abscissa and ordinate change at the same rate is.

(4, 2)

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(- 4, 2)

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(2, 4)

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(- 2, - 4)

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Solution

The correct option is D $(2, 4)$
Given, $y^{2} = 8 x$
$\Rightarrow 2 y \frac{d y}{d t} = 8 \frac{d x}{d t}$
Rate of change of abscissa and ordinate are same when $2 y = 8$
$\Rightarrow y = 4$
$∴$ At $(2, 4)$ abscissa and ordinate change at the same rate.
Hence, option C.

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