Question

Any help with the question above??? The graph is attached... ONLY REAL ANSWERS, NO GUESSING!

Answer 1

Answer:

  see below

Step-by-step explanation:

The co-vertex is 2 units from center in the x-direction, so the denominator of the x-term will be 2² = 4. Only two answer choices match.

The major axis is parallel to the y-axis, so the foci will have different y-coordinates. Of the two answer choices just found, only one of them has the foci on a vertical line: the choice shown below.

_____

If you actually want to write the equation, note that the center of the ellipse is (-4, -3), and the semi-major axis is 4 units in the y-direction. The standard-form equation will be ...

  (x+4)/2² +(y+3)/4² = 1

The distance from center to a focus will be the root of the difference of the denominators, so is √(16-4) = 2√3. That is the distance along the semi-major axis, so puts the foci at (-4, -3±2√3).