Find the Cartesian equation of the curve given by the following parametric equation:
x= 2 sin t-1, y=5cos t+4, 0<t<2pi
I understand that this can be done using substitution and utilising well-known trig identities. I ended up getting an equation for y, as follows:
y=219−5x However, when I checked the solution, I was disappointed to find that the intended solution would be in the form of an equation for a circle. What I want to know is: what, in the question, implied that this is what I should have done, rather than write a cartesian equation in the form "y=..."? I would hate to make this mistake in an exam, so if anyone could point out my mistake(s), I would really appreciate it