Eliminate the parameter t from the following x 4 cos t 2 y

Eliminate the parameter t from the following, x = 4 cos t - 2, y = 4 sin t + 1

x = 4 cos t - 2

y = 4 sin t + 1

from equation 1

x = 4 cos t - 2

adding 2 on both sides

x+2 = 4 cos t

dividing both sides by 4

( x+ 2) / 4 = cos t

t = cos^-1 ( x+2) / 4

from equation 2

y = 4 sin t + 1

y-1 = 4 sin t

sin^-1 ( y-1) / 4 = t

setting both t\'s equal to each other

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

sin^-1 (y-1) = cos^-1 (x+2)

y-1 = sin ( cos^-1 (x+2) )

y = sin ( cos^-1 (x+2) ) + 1