SOLUTION: Eliminate the parameter in the following set of parametric equations to find a Cartesian equation of the curve. Graph the curve that the parametric equations represent and indicat

Algebra ->  Test -> SOLUTION: Eliminate the parameter in the following set of parametric equations to find a Cartesian equation of the curve. Graph the curve that the parametric equations represent and indicat      Log On


   

Question 967343: Eliminate the parameter in the following set of parametric equations to find a Cartesian equation of the curve.
Graph the curve that the parametric equations represent and indicate the orientation. What type of conic section
does the curve represent?
x = 3 + 2 sin(t) y = 3 cos(t)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
sin(t) = (x-3)/2

cos(t) = y/3

sin^2(t) + cos^2(t) = 1 becomes:

((x-3)/2)^2 + (y/3)^2 = 1 which becomes:

(x-3)^2 / 2^2 + y^2 / 3^2 = 1 which becomes:

(x-3)^2 / 4 + y^2 / 9 = 1

this looks like it's the equation of an ellipse.

the graph of that equation is shown below:

in the graph, 3 (x,y) pairs were shown to be on the graph of the equation.

these points were derived from the parametric equations for x and y.

this confirmed that the graph is an accurate representation of the parametric equations.

the 3 points were based on t = 0, t = 45 degrees, t = 270 degrees.

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