In an ellipse, the distances between its foci is `6` and minor axis is `8`. Then its eccentricity is

Options

A. `3/5`
B. `1/2`
C. `4/5`
D. `1/sqrt5`

Answer

To solve the problem step by step, we will follow the information given and apply the formulas related to an ellipse.

### Step 1: Understand the given information
We know the following:
- The distance between the foci of the ellipse is `6`.
- The length of the minor axis is `8`.

### Step 2: Relate the distance between the foci to eccentricity
The distance between the foci of an ellipse is given by the formula:
\[ 2c = 6 \]
where \(c\) is the distance from the center to each focus. Therefore, we can find \(c\):
\[ c = \frac{6}{2} = 3 \]

### Step 3: Find the semi-minor axis
The length of the minor axis is given as `8`, which means the semi-minor axis \(b\) is:
\[ b = \frac{8}{2} = 4 \]

### Step 4: Use the relationship between \(a\), \(b\), and \(c\)
In an ellipse, the relationship between the semi-major axis \(a\), semi-minor axis \(b\), and the distance to the foci \(c\) is given by:
\[ c^2 = a^2 - b^2 \]
We already know \(c\) and \(b\):
\[ 3^2 = a^2 - 4^2 \]
This simplifies to:
\[ 9 = a^2 - 16 \]
Thus, we can solve for \(a^2\):
\[ a^2 = 9 + 16 = 25 \]
So, we find:
\[ a = \sqrt{25} = 5 \]

### Step 5: Calculate the eccentricity
The eccentricity \(e\) of an ellipse is defined as:
\[ e = \frac{c}{a} \]
Substituting the values we found:
\[ e = \frac{3}{5} \]

### Conclusion
The eccentricity of the ellipse is:
\[ \boxed{\frac{3}{5}} \]