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

### 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)

## Answer ( 1 )

Answer Above.