Deriving the Equation of a Circle Using the Pythagorean Theorem

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Mathematics
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1st - 6th Grade
•
Hard
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7 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical theorem is used to derive the equation of a circle centered at the origin?
Binomial Theorem
Fermat's Last Theorem
Pythagorean Theorem
Fundamental Theorem of Calculus
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the term for the distance from the center of a circle to any point on the circle?
Chord
Radius
Circumference
Diameter
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which equation represents a circle centered at the origin with radius r?
x^2 + y^2 = r^2
x + y = r
x^2 + y = r
x^2 - y^2 = r^2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If a circle is centered at the origin and passes through the point (6, 8), what is the radius of the circle?
8
10
6
12
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you determine if a point lies on a given circle?
Check if the point satisfies the circle's equation
Find the midpoint between the point and the center
Calculate the slope of the line through the point and the center
Measure the distance from the point to the center
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the equation of a circle with a radius of 8 centered at the origin?
x^2 + y^2 = 64
x^2 + y^2 = 16
x^2 + y^2 = 32
x^2 + y^2 = 8
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the equation of a circle that passes through a specific point?
Determine the circumference of the circle
Calculate the slope of the line through the point
Draw a right triangle using the point
Find the midpoint of the line segment from the origin to the point
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