Equations of Circles
Flashcard
•
Mathematics
•
10th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the standard form of the equation of a circle?
Back
The standard form of the equation of a circle is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.
2.
FLASHCARD QUESTION
Front
How do you find the center of a circle from its equation?
Back
The center of a circle in the equation (x-h)² + (y-k)² = r² is given by the point (h, k).
3.
FLASHCARD QUESTION
Front
What is the radius of a circle in the equation (x-3)² + (y-2)² = 16?
Back
The radius is 4, since r² = 16, thus r = √16 = 4.
4.
FLASHCARD QUESTION
Front
What does the equation x² + y² = 25 represent?
Back
This represents a circle centered at (0, 0) with a radius of 5, since r² = 25.
5.
FLASHCARD QUESTION
Front
If the center of a circle is (2, -3) and the radius is 5, what is the equation of the circle?
Back
The equation is (x-2)² + (y+3)² = 25.
6.
FLASHCARD QUESTION
Front
What is the distance between the center (1, 1) and a point (4, 5) on the circle?
Back
The distance is 5, calculated using the distance formula: √((4-1)² + (5-1)²) = √(9 + 16) = √25 = 5.
7.
FLASHCARD QUESTION
Front
What is the significance of the value on the right side of the equation in a circle's equation?
Back
The value on the right side (r²) represents the square of the radius of the circle.
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