Expanding the Equation of a Circle: Finding the Center and Radius

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Mathematics
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9th - 10th Grade
•
Hard
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7 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the general form of the equation of a circle centered at (A, B)?
(x - A)^2 - (y - B)^2 = R^2
(x + A)^2 + (y + B)^2 = R^2
(x + A)^2 - (y + B)^2 = R^2
(x - A)^2 + (y - B)^2 = R^2
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which method is NOT mentioned for expanding the equation of a circle?
Substitution method
Grid method
Long division method
FOIL method
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the rearranged equation, what do the variables G and F replace?
A and B
G and H
X and Y
R and C
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the term 'C' represent in the simplified equation?
The center of the circle
A single numerical value
The radius of the circle
The diameter of the circle
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can the radius of a circle be calculated from the expanded form?
By finding the square root of G^2 + F^2 - C
By multiplying G, F, and C
By adding G and F
By subtracting C from G and F
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example provided, what is the center of the circle for the equation X^2 + Y^2 - 8X + 2Y = 13?
(4, -1)
(-4, 1)
(4, 1)
(-4, -1)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the calculated radius of the circle in the example?
1
2
3
4
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