`x` and `y` co-ordinates of a particle moving in `x-y` plane at some instant of time are `x=2t` and `y=4t`.Here `x` and `y` are in metre and `t` in second. Then
The path of the particle is a…….

Options

A. straight line
B. parabola
C. circle
D. ellipse

Answer

To determine the path of the particle moving in the x-y plane given the equations of motion \( x = 2t \) and \( y = 4t \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the equations of motion**:
We have:
\[ x = 2t \]
\[ y = 4t \]

2. **Express time \( t \) in terms of \( x \)**:
From the equation \( x = 2t \), we can solve for \( t \):
\[ t = \frac{x}{2} \]

3. **Substitute \( t \) into the equation for \( y \)**:
Now, substitute \( t \) into the equation for \( y \):
\[ y = 4t = 4\left(\frac{x}{2}\right) \]
Simplifying this gives:
\[ y = 2x \]

4. **Identify the type of path**:
The equation \( y = 2x \) represents a straight line in the x-y plane. The slope of the line is 2, and it passes through the origin (0,0).

### Conclusion:
The path of the particle is a straight line.