Equations of a Circle
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned
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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.
Tags
CCSS.HSG.GPE.A.1
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 general form (Ax² + Ay² + Bx + Cy + D = 0), rewrite it in standard form and identify (h, k) from (x - h)² + (y - k)² = r².
Tags
CCSS.HSG.GPE.A.1
3.
FLASHCARD QUESTION
Front
What is the radius of a circle in standard form?
Back
In the standard form (x - h)² + (y - k)² = r², the radius r is the square root of the number on the right side of the equation.
Tags
CCSS.HSG.GPE.A.1
4.
FLASHCARD QUESTION
Front
Convert the equation x² + y² - 4x + 6y - 12 = 0 to standard form.
Back
(x - 2)² + (y + 3)² = 25.
Tags
CCSS.HSG.GPE.A.1
5.
FLASHCARD QUESTION
Front
What does the term 'completing the square' mean in the context of circles?
Back
Completing the square is a method used to rewrite a quadratic equation in the form of (x - h)² + (y - k)² = r² by rearranging and adjusting the equation.
Tags
CCSS.HSG.GPE.A.1
6.
FLASHCARD QUESTION
Front
What is the significance of the center of a circle?
Back
The center of a circle is the point from which all points on the circle are equidistant, and it is represented as (h, k) in the standard form.
Tags
CCSS.HSG.GPE.A.1
7.
FLASHCARD QUESTION
Front
How do you determine the radius from the equation of a circle?
Back
The radius can be determined from the standard form (x - h)² + (y - k)² = r² by taking the square root of r².
Tags
CCSS.HSG.GPE.A.1
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