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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.
