SOLUTION: #9 Identify x = 4sint y = 5cost a) circle b) parabola c) ellipse d) hyperbola e) none of these

Question 122072: #9
Identify x = 4sint
y = 5cost

a) circle
b) parabola
c) ellipse
d) hyperbola
e) none of these

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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:

Replace with . Replace with . This is why we isolated sine and cosine.

Square to get . Square to get .

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)
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