Find frac{dy}{dx},if x = at^2 and y = 2at. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the parametric equations: $x = at^2$ and $y = 2at$. Differentiating $x$ with respect to $t$: $\frac{dx}{dt} = \frac{d}{dt}(at^2) = 2at$. Dif

Vedclass · Accepted Answer

$\frac{1}{t}$

Vedclass · Answer

(A) Given the parametric equations: $x = at^2$ and $y = 2at$. Differentiating $x$ with respect to $t$: $\frac{dx}{dt} = \frac{d}{dt}(at^2) = 2at$. Differentiating $y$ with respect to $t$: $\frac{dy}{dt} = \frac{d}{dt}(2at) = 2a$. Using the chain rule for parametric differentiation: $\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{2a}{2at} = \frac{1}{t}$.

Find $\frac{dy}{dx}$,if $x = at^2$ and $y = 2at$.

Similar Questions

If $x = a \sin \theta$ and $y = b \cos \theta$,then $\frac{d^2y}{dx^2}$ is

If $x = at^2$ and $y = 2at$,then find $y_2$ (where $t \neq 0$).

The position of a point at time $t$ is given by $x = a + bt - ct^2$ and $y = at + bt^2$. Its acceleration at time $t$ is:

If $x = a(t - \frac{1}{t})$ and $y = a(t + \frac{1}{t})$,then $\frac{dy}{dx} = $

If $x = 2 \cos^3 \theta$ and $y = 3 \sin^2 \theta$,then $\frac{dy}{dx} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module