Convert the general form of a circle's equation $$ x^2 + y^2 + 10x - 26y + 169 = 0 $$ to standard form.

The standard form is $$ (x+5)^2 + (y-13)^2 = 25 $$ .

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

The center can be identified as (h, k) from the equation in the form $$ (x-h)^2 + (y-k)^2 = r^2 $$ .

What is the equation of a circle with center (0, 0) and radius 5?

The equation is $$ x^2 + y^2 = 25 $$ .

What does the term $$ (x-h) $$ represent in the equation of a circle?

It represents the horizontal distance from the center of the circle to a point on the circle.

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

The general form is $$ x^2 + y^2 + Dx + Ey + F = 0 $$ .

If a circle has a center at (2, 3) and a radius of 4, what is its equation?

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

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

The area of a circle is given by the formula $$ A = \frac{1}{2} \times \text{radius}^2 $$ .

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

The distance formula is used to find the distance between the center of the circle and any point on the circle.

7.1 Equation of Circles Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the standard equation of a circle?

Back

Tags

CCSS.HSG.GPE.A.1

2.

FLASHCARD QUESTION

Front

Back

This equation represents a circle with center (3, 2) and radius 4 units.

Tags

CCSS.HSG.GPE.A.1

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

4.

FLASHCARD QUESTION

Front

Back

The center of the circle is (-4, 2).

Tags

CCSS.HSG.GPE.A.1

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.GPE.A.1

6.

FLASHCARD QUESTION

Front

Back

The number on the right side represents the square of the radius of the circle.

Tags

CCSS.HSG.GPE.A.1

7.

FLASHCARD QUESTION

Front

If the radius of a circle is 3, what is the equation of the circle centered at (1, -1)?

Back

Tags

CCSS.HSG.GPE.A.1

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