A-maths!

1. x = √(4 - t²) ───── (1)

y = t² + 2 ───── (2)

From (2):

t² = y - 2 ───── (#)

sub (#) into (1)

i.e. x = √[4 - (y - 2)]

x = √(6 - y)

x² = 6 - y



2. x = 2cost + sint ───── (1)

y = cost - 2sint ───── (2)

(1)² + (2)²:

x² + y² = (2cost + sint)² + (cost - 2sint)²

x² + y² = 4cos²t + 4sintcost + sin²t + cos²t - 4sintcost + 4sin²t

x² + y² = 4(cos²t + sin²t) + (sin²t + cos²t) + 4sintcost - 4sintcost

x² + y² = 4(1) + 1 + 0

x² + y² = 5