Question

Write the standard equation of the ellipse with center at the origin, and vertices at (-4,0), (4,0), (0, -3), and (0,3).

Answer 1

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Answer:

  (a)  x^2/16 +y^2/9 = 1

Step-by-step explanation:

The form for the equation of an ellipse centered at the origin is ...

  (x/(semi-x-axis))^2 +(y/(semi-y-axis))^2 = 1

The vertex values tell you the semi-x-axis is 4 units, and the semi-y-axis is 3 units. Then you have ...

  (x/4)^2 +(y/3)^2 = 1

  x^2/16 +y^2/9 = 1

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In case you don't remember that form, you can try any of the points in the equations. The equation that works will quickly become apparent.