Final answer:
To eliminate the parameter, we need to express either x or y in terms of the other variable. From the given equations x = 5sin(t) and y = 3cos(t), we can substitute these expressions and simplify to obtain x² + y² = 34. None of the given options matches this equation.
Step-by-step explanation:
To eliminate the parameter, we need to express either x or y in terms of the other variable. From the given equations, we can solve for x in terms of t: x = 5sin(t). Now we can substitute this expression into the equation y = 3cos(t) to get y in terms of t as well: y = 3cos(t).
Now we have the parametric equations x = 5sin(t) and y = 3cos(t) in terms of t. To eliminate t, we can square both equations and add them together:
x² + y² = (5sin(t))² + (3cos(t))²
Simplifying further, we get:
x² + y² = 25sin²(t) + 9cos²(t)
Since sin²(t) + cos²(t) = 1, we can substitute this into the equation:
x² + y² = 25(1) + 9(1) = 25 + 9 = 34
Therefore, the correct equation after eliminating the parameter is x² + y² = 34, which is not one of the given options. None of the options A, B, C, or D represents the equation obtained after eliminating the parameter.