# Parametrics/Rates of Change (1 Viewer)

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#### fan96

##### 617 pages
It is given that the $y$ co-ordinate of $P$ increases at one unit per second. That is,

$\frac{d(ap^2)}{dt} = 1$

We want to use part iii) to answer the question. That means we need to find $dp/dt$.

$\frac{dp}{dt} = \frac{d(ap^2)}{dt} \cdot \frac{dp}{d(ap^2)}$

And,

$\frac{dp}{d(ap^2)} = \frac{1}{\frac{d}{dp} ap^2} = \frac{1}{2ap}$

So,

$\frac{dp}{dt} = 1 \cdot \frac{1}{2ap} = \frac{1}{2ap}$

Then substitute back into iii) and a similar process for $Q$ will give

$\frac{d(aq^2)}{dt} = -\frac{q^2}{p^2}$