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which of the following is the equation for the graph shown?

(Third Option)

Step-by-step explanation:

Equation Of The Ellipse

The characteristic shape of an ellipse can be identified in the image provided in the question. Since it's centered in the origin, we can say its equation is

From the presented options, only the first and third correspond to the equation of an ellipse. To help us to choose which is the correct one, we look at the x-intercepts, some more than 5 units. When x is set to that value, y should be zero. It can only happen if

We are sure it's not the first option since cannot be 5, let's compute

Now we're sure the third option is the only correct candidate. Let's verify with the y-intercept, which can only happen when x=0. It gives us

Answer the equation for the graph shown is

Third Option