Find the equation of parabola
(i) having its vertex at A(1,0) and focus at S(3,0)
(ii) having its focus at S(2,5) and one of the extremities of latus rectum is A (4,5)

Explanation

To find the equations of the parabolas based on the given conditions, we will solve each part step by step.

### Part (i): Vertex at A(1,0) and Focus at S(3,0)

1. **Identify the vertex and focus**:
The vertex \( A \) is at \( (1, 0) \) and the focus \( S \) is at \( (3, 0) \).

2. **Determine the orientation of the parabola**:
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