What is the radius of a circle with the equation $$(x - 1)^2 + (y + 4)^2 = 36$$ ?

The radius of the circle is 6, since $$r = \text{sqrt}(36) = 6$$ .

What does the equation $$(x - 3)^2 + (y + 2)^2 = 9$$ represent?

This equation represents a circle with center (3, -2) and radius 3.

What is the distance between the center of the circle at (1, 2) and a point (4, 6)?

The distance is calculated using the distance formula: $$d = \text{sqrt}((4 - 1)^2 + (6 - 2)^2) = \text{sqrt}(9 + 16) = 5$$ .

What is the equation of a circle centered at (-1, -5) with a radius of 5?

The equation is $$(x + 1)^2 + (y + 5)^2 = 25$$ .

What does the term 'diameter' refer to in relation to a circle?

The diameter is twice the radius of the circle, representing the longest distance across the circle through the center.

How can you determine if a point lies inside, on, or outside a circle?

Substitute the point's coordinates into the circle's equation. If the result is less than, equal to, or greater than the radius squared, the point is inside, on, or outside the circle, respectively.

What is the significance of the constant in the circle equation?

The constant on the right side of the equation represents the square of the radius of the circle.

What is the equation of a circle with center at (2, 0) and radius 4?

The equation is $$(x - 2)^2 + y^2 = 16$$ .

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

The area of a circle is given by the formula $$A = \text{pi} \times r^2$$ , where r is the radius.

Equation of a Circle Review 1 - Flashcardizz Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

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

Back

2.

FLASHCARD QUESTION

Front

What do the variables (h, k) represent in the circle equation?

Back

The variables (h, k) represent the coordinates of the center of the circle.

3.

FLASHCARD QUESTION

Front

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

Back

4.

FLASHCARD QUESTION

Front

Back

The center of the circle is (-2, 3).

5.

FLASHCARD QUESTION

Front

If a circle has a center at (0, 0) and a radius of 5, what is its equation?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

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

Back

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