Card 1 of 20
EasyStudy card 1
Prompt
What is standard form for a circle?
Answer
\((x-h)^2+(y-k)^2=r^2\).
MathChapter 19: Circles
Flashcards
Equations of Circles Flashcards
Twenty concise cards on standard form, completing squares, diameter endpoints, and coordinate applications.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What is the center in standard form?
Answer
\((h,k)\).
Card 3 of 20
EasyStudy card 3
Prompt
How is radius read from standard form?
Answer
Take the positive square root of the right side.
Card 4 of 20
EasyStudy card 4
Prompt
What center does (x+3)² show?
Answer
An x-coordinate of -3.
Card 5 of 20
EasyStudy card 5
Prompt
What center does (y-5)² show?
Answer
A y-coordinate of 5.
Card 6 of 20
EasyStudy card 6
Prompt
What completes x²+bx to a square?
Answer
Add \((b/2)^2\).
Card 7 of 20
EasyStudy card 7
Prompt
What must happen when completing a square in an equation?
Answer
Add the same value to both sides.
Card 8 of 20
MediumStudy card 8
Prompt
How is a circle center found from diameter endpoints?
Answer
Take their midpoint.
Card 9 of 20
MediumStudy card 9
Prompt
How is radius found from diameter endpoints?
Answer
Take half their distance, or distance from midpoint to one endpoint.
Card 10 of 20
MediumStudy card 10
Prompt
For center (h,k), what radius gives y-axis tangency?
Answer
\(|h|\).
Card 11 of 20
MediumStudy card 11
Prompt
For center (h,k), what radius gives x-axis tangency?
Answer
\(|k|\).
Card 12 of 20
MediumStudy card 12
Prompt
How can circle area be read quickly from standard form?
Answer
The right side is r², so multiply it by π.
Card 13 of 20
MediumStudy card 13
Prompt
What must r² be for a real nondegenerate circle?
Answer
Positive.
Card 14 of 20
MediumStudy card 14
Prompt
What does translating a circle change?
Answer
The center, not the radius.
Card 15 of 20
MediumStudy card 15
Prompt
What is the leftmost x-coordinate of a circle?
Answer
\(h-r\).
Card 16 of 20
MediumStudy card 16
Prompt
What is the highest y-coordinate of a circle?
Answer
\(k+r\).
Card 17 of 20
HardStudy card 17
Prompt
Center (-2,4), radius 3: equation?
Answer
\((x+2)^2+(y-4)^2=9\).
Card 18 of 20
HardStudy card 18
Prompt
Complete x²-8x: what is added?
Answer
16.
Card 19 of 20
HardStudy card 19
Prompt
Diameter endpoints (-5,1) and (3,1): center and radius?
Answer
Center (-1,1), radius 4.
Card 20 of 20
HardStudy card 20
Prompt
Why is the right side 49 not radius 49?
Answer
It represents r², so the radius is 7.
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