Find the eccentricity of the ellipse of which the major axis is double the minor axis.

Answer

To find the eccentricity of the ellipse where the major axis is double the minor axis, we can follow these steps:

### Step 1: Define the ellipse equation
We start with the standard form of the ellipse equation:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
where \( a \) is the semi-major axis and \( b \) is the semi-minor axis.

### Step 2: Relate the axes
According to the problem, the major axis is double the minor axis. This can be expressed mathematically as:
\[ 2a = 2b \implies a = 2b \]

### Step 3: Substitute the relation into the equation
We can substitute \( a = 2b \) into the equation for \( a^2 \):
\[ a^2 = (2b)^2 = 4b^2 \]

### Step 4: Use the eccentricity formula
The eccentricity \( e \) of an ellipse is given by the formula:
\[ e = \sqrt{1 - \frac{b^2}{a^2}} \]
Substituting \( a^2 = 4b^2 \) into the formula:
\[ e = \sqrt{1 - \frac{b^2}{4b^2}} = \sqrt{1 - \frac{1}{4}} = \sqrt{\frac{3}{4}} \]

### Step 5: Simplify the expression
Now, we simplify the expression for \( e \):
\[ e = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2} \]

### Conclusion
Thus, the eccentricity of the ellipse is:
\[ \boxed{\frac{\sqrt{3}}{2}} \]