Rewrite this circle's equation in standard form by completing the square: $$x^2+2x+y^2-10y+22=0$$

$$\text{The standard form is } (x+1)^2+(y-5)^2=4$$ .

Which graph matches the equation: $$ (x-2)^2+(y-3)^2=1 $$ ?

$$\text{Graph that shows a circle centered at (2,3) with radius 1.}$$

What is the radius of a circle if the equation is given as $$ (x-5)^2+(y+2)^2=9 $$ ?

$$\text{The radius is } 3 \text{ (since } r^2 = 9 \text{, thus } r = \text{sqrt}(9) = 3)$$ .

What is the diameter of a circle if the radius is 4?

$$\text{The diameter is } 8 \text{ (since diameter } = 2 \times radius)$$ .

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

$$\text{The equation is } x^2+y^2=25$$ .

What does completing the square involve when rewriting a circle's equation?

$$\text{It involves rearranging the equation to isolate } x \text{ and } y \text{ terms and forming perfect squares.}$$

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

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

What is the significance of the term 'r' in the circle's equation?

$$r \text{ represents the radius of the circle, which is the distance from the center to any point on the circumference.}$$

What is the relationship between the center and radius in the equation of a circle?

$$\text{The center (h, k) and radius r define the size and position of the circle in the coordinate plane.}$$

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

$$\text{By completing the square for both } x \text{ and } y \text{ terms.}$$

Equations of Circles Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the standard equation of a circle?

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

Front

What do the variables h and k represent in the standard form of a circle’s equation?

Back

4.

FLASHCARD QUESTION

Front

What is the standard equation of a circle with the center at (3,-4) and a radius of 2?

Back

5.

FLASHCARD QUESTION

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Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

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

Back

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