If x and y are connected parametrically by the equation,


If $x$ and $y$ are connected parametrically by the equation, without eliminating the parameter, find $\frac{d y}{d x}$.

$x=2 a t^{2}, y=a t^{4}$


The given equations are $x=2 a t^{2}$ and $y=a t^{4}$

Then, $\frac{d x}{d t}=\frac{d}{d t}\left(2 a t^{2}\right)=2 a \cdot \frac{d}{d t}\left(t^{2}\right)=2 a \cdot 2 t=4 a t$

$\frac{d y}{d t}=\frac{d}{d t}\left(a t^{4}\right)=a \cdot \frac{d}{d t}\left(t^{4}\right)=a \cdot 4 \cdot t^{3}=4 a t^{3}$

$\therefore \frac{d y}{d x}=\frac{\left(\frac{d y}{d t}\right)}{\left(\frac{d x}{d t}\right)}=\frac{4 a t^{3}}{4 a t}=t^{2}$

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now