The standard equation of an ellipse with vertices (-5,2) and (3,2) and minor axis of length 6 is

Options

A. `((x+1)^(2))/(16)+((y-2)^(2))/(9)=1`
B. `((x-1)^(2))/(9)+((y+2)^(2))/(16)=1`
C. `((x+1)^(2))/(9)+((y-2)^(2))/(16)=1`
D. `((x-1)^(2))/(16)+((y-2)^(2))/(9)=1`

Explanation

To find the standard equation of the ellipse with given vertices and minor axis length, we can follow these steps:

### Step 1: Identify the vertices and calculate the center
The vertices of the ellipse are given as (-5, 2) and (3, 2). The center of the ellipse can be found by calculating the midpoint of these two vertices.

\[ \text{Center} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{-5 + 3}{2}, \frac{2 + 2}{2} \right) = \left( \frac{-2}{2}, \frac{4}{2} \right) = (-1, 2) \]
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