Question

explain the given problem

Answer 1

$\large\rm { \vec{v} = 2y \ \hat{i} + 4 \ \hat{j}}$

Now,

$\large\rm { v_{x} = 2y}$

$\large\rm { \implies \frac{dx}{dt} = 2y }$

$\large\rm { v_{y} = 4}$

$\large\rm { \implies \frac{dy}{dt} = 4 }$

Now,

$\large\rm { \frac{dy}{dx} = \frac{4}{2y}}$

$\large\rm { 2y \ dy = 4dx }$

Integrating both sides,

$\large\rm { \displaystyle\int \rm{y \ dy} = 2 \displaystyle\int \rm{dx}}$

$\large\bf { \therefore y^{2} = 4x}$

Hence, option (iii) is correct.

Answer 2

Answer: option 3

Explanation: see the pic