Question 1

Given the circle shown in the first image, what is the equation of the circle with center at $$(2, 4)$$ and radius $$7$$?

Accepted Answer

$$ (x-2)^2$ + (y-4)^2$ = 49 $$

Question 2

What is the equation of the circle shown in the second image, with center at $$(-2, 4)$$ and radius $$7$$?

Accepted Answer

$$ (x+2)^2$ + (y-4)^2$ = 49 $$

Question 3

For the third image, what is the equation of the circle with center at $$(-2, -4)$$ and radius $$7$$?

Accepted Answer

$$ (x+2)^2$ + (y+4)^2$ = 49 $$

Question 4

Which of the following is the general equation of a circle with center $$(a, b)$$ and radius $$r$$?

Accepted Answer

$$ (x-a)^2$ + (y-b)^2$ = r^2$ $$

Question 5

A circle has its center at the origin and a radius of $$5. $$What is its equation?

Accepted Answer

$$ x^2$ + y^2$ = 25 $$

Question 6

Given the endpoints of a diameter $$A(7, 10)$$ and $$B(11, -2)$$, what is the center of the circle?

Accepted Answer

$$ (9, 4) $$

Question 7

Given the endpoints of a diameter $$A(7, 10)$$ and $$B(11, -2)$$, what is the length of the radius?

Accepted Answer

$$ \sqrt{52}/2 $$

Question 8

Given the equation $$ (x-3)^2$ + (y-6)^2$ = 49 $$, what are the center and radius of the circle?

Accepted Answer

Center: $$(3, 6)$$, Radius: $$7$$

Question 9

Given the equation $$ x^2$ + 2x + y^2$ - 4y = 9 $$, what is the center of the circle after completing the square?

Accepted Answer

$$( -1, 2 )$$

Question 10

Given the equation $$ x^2$ + 2x + y^2$ - 4y = 9 $$, what is the radius of the circle after completing the square?

Accepted Answer

$$\sqrt{14}$$

Question 11

A real-world application: A circular park has its center at $$(5, -3)$$ and a radius of $$10$$ meters. Which equation models the boundary of the park?

Accepted Answer

$$ (x-5)^2$ + (y+3)^2$ = 100 $$

Question 12

If a circle has the equation $$ (x+4)^2$ + (y-1)^2$ = 36 $$, what is the center and radius?

Accepted Answer

Center: $$(-4, 1)$$, Radius: $$6$$

Question 13

A circular fountain is centered at $$(0, 0)$$ and has a radius of $$12$$ meters. What is the equation of the fountain's edge?

Accepted Answer

$$ x^2$ + y^2$ = 144 $$

Question 14

Which of the following best describes the process of finding the equation of a circle given the endpoints of a diameter?

Accepted Answer

Find the midpoint for the center, calculate the distance between endpoints for the diameter, then use half the distance as the radius.

Step-by-Step Guidance: Circle Equations in College Algebra

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