Circles: Write the equation from a graph
Flashcard
•
Mathematics
•
10th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the standard equation of a circle?
Back
The standard equation of a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².
2.
FLASHCARD QUESTION
Front
How do you determine 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 does the radius of a circle represent in its equation?
Back
The radius r in the equation (x - h)² + (y - k)² = r² represents the distance from the center (h, k) to any point on the circle.
4.
FLASHCARD QUESTION
Front
If the equation of a circle is (x + 3)² + (y - 2)² = 16, what is the center and radius?
Back
The center is (-3, 2) and the radius is 4.
5.
FLASHCARD QUESTION
Front
What is the relationship between the diameter and radius of a circle?
Back
The diameter is twice the radius (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 significance of the value on the right side of the equation (x - h)² + (y - k)² = r²?
Back
The value on the right side (r²) represents the square of the radius, indicating the size of the circle.
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