Question

A pair of parametric equations is given.

x = sec(t), y = tan^2(t), 0 ≤ t < pi/2

Find a rectangular-coordinate equation for the curve by eliminating the parameter

Answer 1

To eliminate the parameter and express the curve in rectangular coordinates, we can use the trigonometric identity that relates sec(t) and tan(t).

The identity is: sec^2(t) = 1 + tan^2(t)

Using this identity, we can rewrite the equation for x in terms of y:

x = sec(t)
x = √(1 + tan^2(t))

Now we have a rectangular-coordinate equation for the curve, where x is expressed in terms of y:

x = √(1 + y)

This equation represents the curve when 0 ≤ t < π/2.

Answer 2

y

2

+

1

=

x

2

Step-by-step explanation:

use the identity

tan

2

+

1

=

sec

2

so here that means that

y

2

+

1

=

x

2

hyperbola!

Step-by-step explanation: