PRE CALCULUS Conic Sections and Parametric Equations 2

Question 1

What is the eccentricity of a circle?

Accepted Answer

0

Answer

A circle has eccentricity e = 0, meaning both foci coincide at the center.

Question 2

For the hyperbola x²/16 − y²/9 = 1, what are the equations of the asymptotes?

Accepted Answer

y = ±(3/4)x

Answer

The asymptotes of x²/a² − y²/b² = 1 are y = ±(b/a)x, so y = ±(3/4)x.

Question 3

Which parametric equations trace a circle of radius 3 centered at the origin?

Accepted Answer

x = 3cos(t), y = 3sin(t)

Answer

x = 3cos(t) and y = 3sin(t) satisfy x² + y² = 9, tracing a circle of radius 3.

Question 4

The directrix of the parabola x² = 8y is:

Accepted Answer

y = −2

Answer

From x² = 4py with 4p = 8, p = 2; the directrix is y = −p = −2.

Question 5

To eliminate the parameter t from x = t + 1, y = t² − 3, what is the Cartesian equation?

Accepted Answer

y = (x−1)² − 3

Answer

Solving x = t + 1 gives t = x − 1; substituting into y = t² − 3 yields y = (x−1)² − 3.

PRE CALCULUS Practice Test