M12: Quadratic Relations and Systems of Equations

Question 1

What is the standard form equation of a circle?

Answer 1

(x - h)^2+ (y - k)^2= r^2

Question 2

If you solve (x - h)^2+ (y - k)^2= r^2 for r, your equation should be:

Answer 2

r = √(x -h) ^2+ (y - k)^2

Question 3

Write the equation for a circle with center C(-3, 2) and radius r = 4

Answer 3

Substitute -3 for h, 2 for k, and 4 for r into the general equation and simplify.

(x - (-3))^2+ (y - 2)^2 = 4^2
(x + 3)^2 + (y - 2)^2 = 16

Question 4

What is the standard form of a parabola?

Answer 4

(x - h)2 = 4p (y - k)

Question 5

What is the directrix

Answer 5

a fixed line used in describing a curve or surface

Question 6

Why do we use a directrix of a parabola?

Answer 6

A parabola is a focus of points equidistant from both 1) a single point, called the focus of the parabola, and 2) a line, called the directrix of the parabola.