How do you identify the center and radius from the equation $$(x+5)^2 + (y+13)^2 = 8$$ ?

The center is (-5, -13) and the radius is $$\text{sqrt}(8)$$ .

What is the relationship between the center and the tangent line to a circle?

The radius drawn to the point of tangency is perpendicular to the tangent line.

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

Use the formula $$(x-h)^2 + (y-k)^2 = r^2$$ , substituting the center (h, k) and radius r.

What does it mean if the radius of a circle is zero?

If the radius is zero, the circle is reduced to a single point, which is the center.

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

Calculate the distance from the point to the center. If it's less than r, inside; equal to r, on; greater than r, outside.

What is the equation of a circle with center (1, -3) and radius 4?

The equation is $$(x-1)^2 + (y+3)^2 = 16$$ .

How do you find the center of a circle from its equation in general form $$x^2 + y^2 + 28x - 18y + 252 = 0$$ ?

Complete the square for x and y to find the center: Center is (-14, 9).

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

Changing the center (h, k) in the equation $$(x-h)^2 + (y-k)^2 = r^2$$ shifts the circle's position without altering its size.

Equations of Circles Flashcards

Student preview

15 questions

Show all answers

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 radius of a circle given its center and a point on the circle?

Back

Tags

CCSS.HSG.GPE.A.1

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

4.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

5.

FLASHCARD QUESTION

Front

What is the significance of the radius in the equation of a circle?

Back

The radius (r) determines the size of the circle; it is the distance from the center to any point on the circle.

Tags

CCSS.HSG.GPE.A.1

6.

FLASHCARD QUESTION

Front

Given the center (3, 10) and a point (8, 11), how do you find the equation of the circle?

Back

Tags

CCSS.HSG.GPE.A.1

7.

FLASHCARD QUESTION

Front

What is the equation of a circle with center (-16, -8) and a radius of 3?

Back

Tags

CCSS.HSG.GPE.A.1

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