Identify the curve of the parametric trig functions?

Question

gahhh this sucks

x = 5 + 2cos(t)

y = 2 + 3sin(t)

show the steps please

thanks a bunch in advance!

Answer 1

(x-5)/2 =cos t

(y-2)/ 3 =sin t

cos^2t +sin^2t = 1 =(x-5)^2 / 4 + (y-2)^2 /9 =1

The curve is an ellipse with center (5,2), major axis parallel to the y=axis and equal to 6, minor axis parallel to x-axis and equal to 4.