Find the equation to the ellipse with axes as the axes of coordinates.
major axis = 6, minor axis = 4,

Answer

To find the equation of the ellipse with the given parameters, we will follow these steps:

### Step 1: Identify the lengths of the axes
The major axis is given as 6 units and the minor axis is given as 4 units.

### Step 2: Determine the semi-major and semi-minor axes
- The length of the semi-major axis \( a \) is half of the major axis:
\[ a = \frac{6}{2} = 3 \]
- The length of the semi-minor axis \( b \) is half of the minor axis:
\[ b = \frac{4}{2} = 2 \]

### Step 3: Write the standard form of the ellipse equation
The standard equation of an ellipse with its major axis along the x-axis is given by:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]

### Step 4: Substitute the values of \( a \) and \( b \)
Now, substitute \( a = 3 \) and \( b = 2 \) into the standard equation:
\[ \frac{x^2}{3^2} + \frac{y^2}{2^2} = 1 \]
This simplifies to:
\[ \frac{x^2}{9} + \frac{y^2}{4} = 1 \]

### Final Equation
Thus, the equation of the ellipse is:
\[ \frac{x^2}{9} + \frac{y^2}{4} = 1 \]

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