Question 1

Given the equation of a circle $$(x-6)^2 + (y+7)^2 = 49$$, what is the center and radius of the circle?

Accepted Answer

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

Question 2

Which of the following is the general form of the equation $$(x-6)^2 + (y+7)^2 = 49$$?

Accepted Answer

Question 3

If the equation of a circle is $$(x-h)^2 + (y-k)^2 = r^2$$, what do the values $$h$$, $$k$$, and $$r$$ represent?

Accepted Answer

$$h$$ and $$k$$ are the coordinates of the center, $$r is $$the radius

Question 4

A circle has the equation $$(x-6)^2 + (y+7)^2 = 49. $$Which point lies on the circle?

Accepted Answer

Question 5

What is the distance from the center of the circle $$(x-6)^2 + (y+7)^2 = 49 to $$the point $$(6, 0)$$?

Accepted Answer

$$7$$

Question 6

If the radius of a circle is $$7$$, what is the area of the circle?

Accepted Answer

$$49\pi$$

Question 7

Which of the following equations represents a circle with center $$(6, -7)$$ and radius $$7$$?

Accepted Answer

$$(x-6)^2$$ + $$(y+7)^2 = 49$

Question 8

If the equation of a circle is $$(x-6)^2 + (y+7)^2 = 49$$, what is the diameter of the circle?

Accepted Answer

$$14$$

Question 9

Which transformation maps the circle $$(x-6)^2 + (y+7)^2 = 49 to $$the circle $$(x-6)^2 + (y+2)^2 = 49$$?

Accepted Answer

Translation $$5$$ units down

Question 10

A circle has center $$(6, -7)$$ and radius $$7. $$What is the equation of the circle in standard form?

Accepted Answer

$$(x-6)^2$$ + $$(y+7)^2 = 49$

Equations of Circles: Finding Center and Radius

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