Math / Geometry

QuestionQuestion Find the center and radius of the circle represented by the equation below. $(x-13)^{2}+(y+11)^{2}=361$
Answer Attempt 1 out of 2
Center: $\square$ $\square$ )
Radius: $\square$

Studdy Solution

STEP 1

What is this asking? We're looking for the center and radius of a circle given its equation. Watch out! Don't mix up the signs of the coordinates of the center!

STEP 2

1. Recall the standard equation of a circle.
2. Identify the center.
3. Determine the radius.

STEP 3

The standard equation of a circle is given by $(x - h)^2 + (y - k)^2 = r^2,$ where $(h, k)$ is the center of the circle and $r$ is its radius.
This equation tells us how far each point $(x, y)$ on the circle is from the center $(h, k)$ .
It's like a distance formula, but specifically for circles!

STEP 4

Let's compare our given equation, $(x - 13)^2 + (y + 11)^2 = 361,$ with the standard equation.
Notice that $y + 11$ can be rewritten as $y - (-11)$ .
This helps us see that $h = \mathbf{13}$ and $k = \mathbf{-11}$ .
So, the center of our circle is $(13, -11)$ .
Remember, the signs in the standard equation are subtractions, so a plus sign in our equation means the corresponding coordinate is negative!

STEP 5

Our equation tells us that $r^2 = \mathbf{361}$ .
To find the radius $r$ , we take the principal square root of both sides: $\sqrt{r^2} = \sqrt{361}.$ This gives us $r = \mathbf{19}$ , since $19 \cdot 19 = 361$ .
The radius is a distance, so it must be positive!

STEP 6

Center: $(13, -11)$ Radius: $19$

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QuestionQuestion Find the center and radius of the circle represented by the equation below. $(x-13)^{2}+(y+11)^{2}=361$
Answer Attempt 1 out of 2
Center: $\square$ $\square$ )
Radius: $\square$

Studdy Solution

STEP 1

What is this asking? We're looking for the center and radius of a circle given its equation. Watch out! Don't mix up the signs of the coordinates of the center!

STEP 2

1. Recall the standard equation of a circle.
2. Identify the center.
3. Determine the radius.

STEP 3

The standard equation of a circle is given by $(x - h)^2 + (y - k)^2 = r^2,$ where $(h, k)$ is the center of the circle and $r$ is its radius.
This equation tells us how far each point $(x, y)$ on the circle is from the center $(h, k)$ .
It's like a distance formula, but specifically for circles!

STEP 4

STEP 5

Our equation tells us that $r^2 = \mathbf{361}$ .
To find the radius $r$ , we take the principal square root of both sides: $\sqrt{r^2} = \sqrt{361}.$ This gives us $r = \mathbf{19}$ , since $19 \cdot 19 = 361$ .
The radius is a distance, so it must be positive!

STEP 6

Center: $(13, -11)$ Radius: $19$

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QuestionQuestion Find the center and radius of the circle represented by the equation below. (x−13)2+(y+11)2=361(x-13)^{2}+(y+11)^{2}=361(x−13)2+(y+11)2=361Answer Attempt 1 out of 2Center: □\square□ □\square□ )Radius: □\square□

Studdy Solution

STEP 1

What is this asking? We're looking for the center and radius of a circle given its equation. Watch out! Don't mix up the signs of the coordinates of the center!

STEP 2

1. Recall the standard equation of a circle.2. Identify the center.3. Determine the radius.

STEP 3

STEP 4

STEP 5

STEP 6

Center: (13,−11)(13, -11)(13,−11) Radius: 191919

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionQuestion Find the center and radius of the circle represented by the equation below. $(x-13)^{2}+(y+11)^{2}=361$
Answer Attempt 1 out of 2
Center: $\square$ $\square$ )
Radius: $\square$

1. Recall the standard equation of a circle.
2. Identify the center.
3. Determine the radius.

Center: $(13, -11)$ Radius: $19$