Question

exam
question 1: standard g.gpe.1
to graph a circle we need to relate circles to which variable(s)?
a. a and b
b. x and y
c. r
d. x
question 2: standard g.gpe.1
which variable changes the properties of a circle?
a. x
b. y
c. r
d. a
question 3: standard g.gpe.1
how can we relate the variables x, y and r within a circle?
a. pythagorean theorem
b. aa~
c. cosine
d. law of sines
question 4: standard g.gpe.1
in the equation ((x - 1)^2 + (y - 4)^2 = 9), the radius is?
a. 4
b. 1
c. -4
d. 3
question 5: standard g.gpe.1
in the equation ((x - 1)^2 + (y - 4)^2 = 9), the center of the circle is?
a. (1, 4)
b. (-1, -4)
c. (4, 1)
d. (1, 9)

Explanation:

Question 1

To graph a circle, we use the coordinate variables \( x \) and \( y \) (for the center and points on the circle) along with the radius \( r \). The variables \( A \) and \( B \) are not standard for circle graphing. So the relevant variables are \( X \) and \( Y \).

The radius \( R \) (or \( r \)) of a circle determines its size (a property), while \( X \) and \( Y \) are coordinates for position (not a property change like size). \( A \) is not a standard circle variable. So \( R \) changes the properties (size) of the circle.

The equation of a circle \((x - h)^2+(y - k)^2 = r^2\) is derived from the Pythagorean theorem, relating the horizontal (\( x - h \)), vertical (\( y - k \)) distances from the center to a point on the circle, and the radius \( r \). AA~ is for similar triangles, cosine and Law of Sines are for trigonometric relationships not directly for circle - \( x,y,r \) relation.

Answer:

b. X and Y

Question 2