Eliminate the parameter to find a Cartesian equation for x = sin 2 t and y = 2 cos t ?

Question

Question:

Eliminate the parameter to find a Cartesian equation for x = sin 2 t and y = 2 cos t ?

Answer:

y2=−4(x−1)
Clarification:
There are numerous approaches to do this. I’ll pick one which depends after utilizing a typical trigonometric character, in particular:
sin2t+cos2t=1

We as of now have an articulation for sin2t – to be specific, x – so all that remaining parts is to control the other articulation to fit that design:
y=2cost
y/2=cost
cos2t=y2/4

Take these two connections and spot them into the trig character:
sin2t+cos2t=1
x+y2/4=1
4x+y2=4
y2=−4x+4 or y2=−4(x−1)
(Incidentally, this shows the outcome is a parabola which opens to one side, with a)

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