calculus parametric curves *need help asap please, thank you!*

Question

Which of the following is the Cartesian equation for the parametric equation x = 2tan(t), y = 5sec(t)? (4 points)

answer choices:

	y = x2 - 9, for x in [-3,3]

Answer 1

First we need to isolate tan(t) and sec(t)

tan(t) = x/2

sec(t) = y/5

We know the identity tan²(t) + 1= sec²(t)

Therefore

(y/5)² = (x/2)² + 1

or

y²/25 = x²/4 + 1 same as y²/25 - x²/4 = 1 which is the second choice

y² = 25(x²/4 + 1)

y = ±5√(x²/4 + 1)

So the second choice is the best choice since the last choice doesn't include ±