Find the equation of that parabol whose :
(i) vertex is (0,0) and focus is (1,0).

Answer

To find the equation of the parabola with a vertex at (0,0) and a focus at (1,0), we can follow these steps:

### Step 1: Identify the vertex and focus
The vertex of the parabola is given as \( V(0, 0) \) and the focus is given as \( F(1, 0) \).

### Step 2: Determine the orientation of the parabola
Since the focus is to the right of the vertex, the parabola opens to the right.

### Step 3: Use the standard form of the parabola
The standard equation of a parabola that opens to the right with its vertex at the origin is given by:
\[ y^2 = 4ax \]
where \( a \) is the distance from the vertex to the focus.

### Step 4: Calculate the value of \( a \)
The distance \( a \) is the distance from the vertex (0,0) to the focus (1,0). Thus:
\[ a = 1 \]

### Step 5: Substitute \( a \) into the standard equation
Now, substituting \( a = 1 \) into the standard equation:
\[ y^2 = 4(1)x \]
which simplifies to:
\[ y^2 = 4x \]

### Conclusion
The equation of the parabola with vertex at (0,0) and focus at (1,0) is:
\[ \boxed{y^2 = 4x} \]