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

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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 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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