Question

A point is in motion along a hyperbola \(y=\frac{10}{x}\) so that its abscissa \(x\) increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate, when the point passes through \((5,2)\)
(A) increases at the rate of \(\frac{1}{2}\) unit per second
(B) decreases at the rate of \(\frac{1}{2}\) unit per second
(C) decreases at the rate of \(\frac{2}{5}\) unit per second
(D) increases at the rate of \(\frac{2}{5}\) unit per second

Answer 1

Ans: (C)
Hint : \(y=\frac{10}{x}, \frac{d x}{d t}=1\) unit/second
$$
\begin{aligned}
\frac{d y}{d t} &=-\frac{10}{x^{2}} \cdot \frac{d x}{d t} \\
&=-\frac{10}{25} \times 1=-\frac{2}{5} \text { unit/sec }
\end{aligned}
$$
decreases at the rate of \(\frac{2}{5}\) unit per second.

Answer 2

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