Circles and ellipses
Flashcard
•
Mathematics
•
9th - 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
To find the center of a circle from its equation in standard form (x - h)² + (y - k)² = r², identify the values of h and k.
3.
FLASHCARD QUESTION
Front
What is the radius of a circle given the equation (x - 2)² + (y + 3)² = 16?
Back
The radius is 4 units, since r² = 16, thus r = √16 = 4.
4.
FLASHCARD QUESTION
Front
What are the coordinates of the center of the circle given by the equation (x + 5)² + (y - 1)² = 9?
Back
The center is (-5, 1).
5.
FLASHCARD QUESTION
Front
What is the relationship between the radius and the area of a circle?
Back
The area A of a circle is given by the formula A = πr², where r is the radius.
6.
FLASHCARD QUESTION
Front
What is the equation of a circle with center (0, 0) and radius 3?
Back
The equation is x² + y² = 9.
7.
FLASHCARD QUESTION
Front
How do you determine if a point lies inside, on, or outside a circle?
Back
Calculate the distance from the point to the center. If the distance is less than the radius, the point is inside; if equal, on; if greater, outside.
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