Equations of Circles
Flashcard
•
Mathematics
•
10th Grade
•
Practice Problem
•
Hard
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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 given 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
If the center of a circle is at (0, 0) and the radius is 5, what is the equation of the circle?
Back
The equation is x² + y² = 25.
5.
FLASHCARD QUESTION
Front
What is the relationship between the diameter and radius of a circle?
Back
The diameter is twice the radius, so d = 2r.
6.
FLASHCARD QUESTION
Front
How do you convert the general form of a circle's equation to standard form?
Back
To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.
7.
FLASHCARD QUESTION
Front
What is the diameter of a circle with the equation (x - 1)² + (y + 2)² = 36?
Back
The diameter is 12, since the radius is √36 = 6, and d = 2r.
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