Search any question & find its solution
Question:
Answered & Verified by Expert
If $x$ and $y$ are connected parametrically by the given equations, without eliminating the parameter. Find $\frac{d y}{d x}$
$x=2 a t^2, y=a t^4$
$x=2 a t^2, y=a t^4$
Solution:
1825 Upvotes
Verified Answer
$\frac{\mathrm{dx}}{\mathrm{dt}}=4 \mathrm{at}, \frac{\mathrm{dy}}{\mathrm{dt}}=4 \mathrm{at}^3 \therefore \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}=\frac{4 \mathrm{at} \mathrm{t}^3}{4 \mathrm{at}}=\mathrm{t}^2$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{t}^2$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{t}^2$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.