Find the equation of parabola whose
Vertex is (2,3) latus rectum is 8 and axis is parallel to x-axis

Answer

To find the equation of the parabola with the given conditions, we will follow these steps:

### Step 1: Identify the vertex and the latus rectum
The vertex of the parabola is given as (2, 3) and the length of the latus rectum is given as 8.

### Step 2: Determine the value of 'a'
The latus rectum (L) of a parabola is related to 'a' by the formula:
\[ L = 4a \]
Given that \( L = 8 \), we can find 'a':
\[ 8 = 4a \]
\[ a = \frac{8}{4} = 2 \]

### Step 3: Write the general equation of the parabola
Since the axis of the parabola is parallel to the x-axis, the general form of the equation of the parabola is:
\[ (y - y_1)^2 = 4a(x - x_1) \]
where \( (x_1, y_1) \) is the vertex.

### Step 4: Substitute the vertex and 'a' into the equation
From the vertex (2, 3), we have:
- \( x_1 = 2 \)
- \( y_1 = 3 \)

Substituting these values and 'a' into the equation:
\[ (y - 3)^2 = 4 \cdot 2 (x - 2) \]
\[ (y - 3)^2 = 8(x - 2) \]

### Step 5: Write the final equation
Thus, the equation of the parabola is:
\[ (y - 3)^2 = 8(x - 2) \]

---