Fill up the following :-
(i) If parabola `y^2=4ax` passes through point `(2,-3)`, then the length of latus rectum is

Answer

To solve the problem, we need to find the length of the latus rectum of the parabola given by the equation \(y^2 = 4ax\) that passes through the point \((2, -3)\).

### Step-by-Step Solution:

1. **Identify the Equation of the Parabola**:
The equation of the parabola is given as \(y^2 = 4ax\). Here, \(4a\) represents the length of the latus rectum.

2. **Substitute the Point into the Equation**:
Since the parabola passes through the point \((2, -3)\), we substitute \(x = 2\) and \(y = -3\) into the parabola's equation:
\[ (-3)^2 = 4a(2) \]

3. **Calculate the Left Side**:
Calculate \((-3)^2\):
\[ 9 = 4a(2) \]

4. **Simplify the Equation**:
Now simplify the equation:
\[ 9 = 8a \]

5. **Solve for \(a\)**:
To find \(a\), divide both sides by 8:
\[ a = \frac{9}{8} \]

6. **Find the Length of the Latus Rectum**:
The length of the latus rectum is given by \(4a\):
\[ 4a = 4 \times \frac{9}{8} = \frac{36}{8} = \frac{9}{2} = 4.5 \]

### Final Answer:
The length of the latus rectum of the parabola is \(4.5\) units.

---