If `x^(2) = 20y` represents a parabola, then the distance of the focus from the vertex of the parabola is

Options

A. 3 units
B. 4 units
C. 5 units
D. 6 units

Answer

To find the distance of the focus from the vertex of the parabola given by the equation \( x^2 = 20y \), we can follow these steps:

### Step 1: Identify the standard form of the parabola
The given equation \( x^2 = 20y \) can be compared with the standard form of a parabola that opens upwards, which is given by:
\[ x^2 = 4ay \]
Here, \( 4a \) is the coefficient of \( y \).

### Step 2: Determine the value of \( a \)
From the equation \( x^2 = 20y \), we can see that:
\[ 4a = 20 \]
To find \( a \), we divide both sides by 4:
\[ a = \frac{20}{4} = 5 \]

### Step 3: Understand the distance from the vertex to the focus
In a parabola, the distance from the vertex to the focus is given by the value \( a \). Since we have calculated \( a \) to be 5, this means that the distance from the vertex to the focus is 5 units.

### Conclusion
Thus, the distance of the focus from the vertex of the parabola \( x^2 = 20y \) is:
\[ \boxed{5 \text{ units}} \]

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