Given the equation $$(x+5)^2 + (y-2)^2 = 135$$ , what is the diameter?

The diameter is $$2\text{√}135$$ .

How do you convert the area of a circle to a numerical value?

To convert the area to a numerical value, substitute the radius into the area formula $$A = \text{π}r^2$$ and calculate.

What is the relationship between the radius and the area of a circle?

The area increases with the square of the radius; if the radius doubles, the area increases by a factor of four.

Given the equation $$x^2 + (y-3)^2 = 81$$ , what is the area?

The area is 254.47 (using $$A = \text{π}r^2$$ with r = 9).

What does the term 'standard form' refer to in the context of a circle?

'Standard form' refers to the specific equation format that clearly identifies the center and radius of the circle.

How can you graph a circle from its equation?

To graph a circle, identify the center (h, k) and radius r from the equation, then plot the center and draw a circle with radius r.

What is the significance of the values h and k in the circle's equation?

The values h and k represent the x and y coordinates of the center of the circle, respectively.

If a circle has an area of 270π, what is the radius?

The radius is $$\text{√}270$$ .

Standard Form of a Circle

Flashcard

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Mathematics

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10th Grade

•

Practice Problem

•

Hard

•

CCSS

HSG.GPE.A.1, 7.G.B.4, HSG.C.B.5

Standards-aligned

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FLASHCARD QUESTION

Front

What is the standard form of a circle's equation?

Back

Tags

CCSS.HSG.GPE.A.1

FLASHCARD QUESTION

Front

How do you find the center of a circle from its equation?

Back

Tags

CCSS.HSG.GPE.A.1

FLASHCARD QUESTION

Front

How do you find the radius of a circle from its equation?

Back

Tags

CCSS.HSG.GPE.A.1

FLASHCARD QUESTION

Front

What is the diameter of a circle in relation to the radius?

Back

Tags

CCSS.7.G.B.4

FLASHCARD QUESTION

Front

What is the area of a circle?

Back

Tags

CCSS.7.G.B.4

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.GPE.A.1

FLASHCARD QUESTION

Front

Back

The center is (2, -3).

Tags

CCSS.HSG.GPE.A.1

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