PRE CALCULUS Conic Sections and Parametric Equations

Question 1

What is the standard form of a circle with center (h, k) and radius r?

Accepted Answer

(x−h)² + (y−k)² = r²

Answer

The standard equation of a circle is (x−h)² + (y−k)² = r², where (h, k) is the center.

Question 2

Which conic section is formed when the cutting plane is parallel to the base of a double cone?

Accepted Answer

Circle

Answer

A horizontal cut parallel to the base of a cone produces a circle.

Question 3

The focus of the parabola y = x² is located at:

Accepted Answer

(0, 1/4)

Answer

Rewriting y = x² as x² = y in form x² = 4py gives 4p = 1, so p = 1/4 and the focus is (0, 1/4).

Question 4

What distinguishes an ellipse from a hyperbola in standard form?

Accepted Answer

Ellipse uses + between terms; hyperbola uses −

Answer

The standard ellipse equation has the form x²/a² + y²/b² = 1, while the hyperbola uses a minus sign.

Question 5

In the ellipse x²/25 + y²/9 = 1, what is the length of the major axis?

Accepted Answer

10

Answer

The major axis has length 2a where a² = 25, so a = 5 and the major axis = 10.

PRE CALCULUS Practice Test