What is the equation of a circle with center at the origin?

The equation of a circle with center at the origin (0, 0) is $$x^2 + y^2 = r^2$$ .

How do you convert the general form of a circle's equation to standard form?

To convert from general form $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ to standard form, complete the square for x and y.

What is the significance of the number on the right side of the circle's equation?

In the equation $$(x-h)^2 + (y-k)^2 = r^2$$ , the number on the right side (r^2) represents the square of the radius.

How can you identify the radius from the equation of a circle?

In the equation $$(x-h)^2 + (y-k)^2 = r^2$$ , the radius can be identified as the square root of the number on the right side, i.e., $$r = \text{sqrt}(r^2)$$ .

What does it mean if the radius is zero in a circle's equation?

If the radius is zero, the circle is reduced to a single point, which is the center (h, k).

How do you graph a circle given its equation?

To graph a circle, plot the center (h, k), then use the radius r to mark points at a distance r in all directions from the center.

What is the effect of changing the center of a circle in its equation?

Changing the center (h, k) in the equation $$(x-h)^2 + (y-k)^2 = r^2$$ moves the circle to a new location on the coordinate plane.

How do you find the equation of a circle given its center and radius?

To find the equation of a circle given center (h, k) and radius r, use the formula $$(x-h)^2 + (y-k)^2 = r^2$$ .

equations of circles Flashcards

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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

Tags

CCSS.HSG.GPE.A.1

2.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

3.

FLASHCARD QUESTION

Front

What does the radius of a circle represent in its equation?

Back

Tags

CCSS.HSG.GPE.A.1

4.

FLASHCARD QUESTION

Front

How do you determine if a point is inside a circle?

Back

Tags

CCSS.HSG.GPE.A.1

5.

FLASHCARD QUESTION

Front

What is the distance formula used for in relation to circles?

Back

The distance formula is used to find the distance between two points, which can help determine the radius of a circle when given endpoints of a diameter.

Tags

CCSS.HSG.GPE.A.1

6.

FLASHCARD QUESTION

Front

How do you find the midpoint of a diameter of a circle?

Back

Tags

CCSS.HSG.GPE.B.6

7.

FLASHCARD QUESTION

Front

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

Back

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