Math / Geometry

QuestionThe equation of a circle is $(x-9)^{2}+(y+8)^{2}=4$ . What are the center and radius of the circle?
Choose 1 answer: (A) The center is $(9,-8)$ and the radius is 2 .
B The center is $(-9,-8)$ and the radius is 2 . (C) The center is $(9,8)$ and the radius is 2 . (D) The center is $(9,-8)$ and the radius is 4 .

Studdy Solution

STEP 1

What is this asking? We're given the equation of a circle and need to find its center and radius! Watch out! Don't mix up the signs of the coordinates of the center.
Remember the standard form of the equation!

STEP 2

1. Recall the Standard Form
2. Identify the Center
3. Determine the Radius

STEP 3

The standard form of the equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center of the circle and $r$ is its radius.
Let's keep this in mind as we analyze the given equation!

STEP 4

Our equation is $(x - 9)^2 + (y + 8)^2 = 4$ .
We can rewrite this as $(x - 9)^2 + (y - (-8))^2 = 4$ .
This helps us see that $h = 9$ and $k = -8$ .

STEP 5

So, the center of the circle is $(9, -8)$ !

STEP 6

Back to our equation, we have $(x - 9)^2 + (y + 8)^2 = 4$ .
Remember, the standard form tells us that the right side of the equation is $r^2$ .

STEP 7

So, we have $r^2 = 4$ .
To find $r$ , we take the principal square root of both sides: $r = \sqrt{4} = 2$ .
Therefore, the radius is $\bf{2}$ !

STEP 8

The center of the circle is $(9, -8)$ and the radius is $2$ .
This matches answer choice (A)!

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Studdy Solution

STEP 1

What is this asking? We're given the equation of a circle and need to find its center and radius! Watch out! Don't mix up the signs of the coordinates of the center.
Remember the standard form of the equation!

STEP 2

1. Recall the Standard Form
2. Identify the Center
3. Determine the Radius

STEP 3

The standard form of the equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center of the circle and $r$ is its radius.
Let's keep this in mind as we analyze the given equation!

STEP 4

Our equation is $(x - 9)^2 + (y + 8)^2 = 4$ .
We can rewrite this as $(x - 9)^2 + (y - (-8))^2 = 4$ .
This helps us see that $h = 9$ and $k = -8$ .

STEP 5

So, the center of the circle is $(9, -8)$ !

STEP 6

Back to our equation, we have $(x - 9)^2 + (y + 8)^2 = 4$ .
Remember, the standard form tells us that the right side of the equation is $r^2$ .

STEP 7

So, we have $r^2 = 4$ .
To find $r$ , we take the principal square root of both sides: $r = \sqrt{4} = 2$ .
Therefore, the radius is $\bf{2}$ !

STEP 8

The center of the circle is $(9, -8)$ and the radius is $2$ .
This matches answer choice (A)!

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Studdy Solution

STEP 1

What is this asking? We're given the equation of a circle and need to find its center and radius! Watch out! Don't mix up the signs of the coordinates of the center.Remember the standard form of the equation!

STEP 2

1. Recall the Standard Form2. Identify the Center3. Determine the Radius

STEP 3

The **standard form** of the equation of a circle is (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2(x−h)2+(y−k)2=r2, where (h,k)(h, k)(h,k) is the **center** of the circle and rrr is its **radius**.Let's keep this in mind as we analyze the given equation!

STEP 4

Our equation is (x−9)2+(y+8)2=4(x - 9)^2 + (y + 8)^2 = 4(x−9)2+(y+8)2=4.We can rewrite this as (x−9)2+(y−(−8))2=4(x - 9)^2 + (y - (-8))^2 = 4(x−9)2+(y−(−8))2=4.This helps us see that h=9h = 9h=9 and k=−8k = -8k=−8.

STEP 5

So, the **center** of the circle is (9,−8)(9, -8)(9,−8)!

STEP 6

Back to our equation, we have (x−9)2+(y+8)2=4(x - 9)^2 + (y + 8)^2 = 4(x−9)2+(y+8)2=4.Remember, the standard form tells us that the right side of the equation is r2r^2r2.

STEP 7

So, we have r2=4r^2 = 4r2=4.To find rrr, we take the **principal square root** of both sides: r=4=2r = \sqrt{4} = 2r=4​=2.Therefore, the **radius** is 2\bf{2}2!

STEP 8

The center of the circle is (9,−8)(9, -8)(9,−8) and the radius is 222.This matches answer choice (A)!

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What is this asking? We're given the equation of a circle and need to find its center and radius! Watch out! Don't mix up the signs of the coordinates of the center.
Remember the standard form of the equation!

1. Recall the Standard Form
2. Identify the Center
3. Determine the Radius

The standard form of the equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center of the circle and $r$ is its radius.
Let's keep this in mind as we analyze the given equation!

Our equation is $(x - 9)^2 + (y + 8)^2 = 4$ .
We can rewrite this as $(x - 9)^2 + (y - (-8))^2 = 4$ .
This helps us see that $h = 9$ and $k = -8$ .

So, the center of the circle is $(9, -8)$ !

Back to our equation, we have $(x - 9)^2 + (y + 8)^2 = 4$ .
Remember, the standard form tells us that the right side of the equation is $r^2$ .

So, we have $r^2 = 4$ .
To find $r$ , we take the principal square root of both sides: $r = \sqrt{4} = 2$ .
Therefore, the radius is $\bf{2}$ !

The center of the circle is $(9, -8)$ and the radius is $2$ .
This matches answer choice (A)!