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Start with the first parametric equation
Divide both sides by 4 to isolate
Start with the second parametric equation
Divide both sides by 5 to isolate
Now we're going to use the trig identity:
. This is why we isolated sine and cosine.
Notice how the equation is now in the form
(note: h and k are equal to zero in this case)
So this shows us that
graphs an ellipse (since the above equation is the general equation of an ellipse).
So this means that the two parametric equations also graph an ellipse. So the answer is C)