Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To find the center of the circle given by the equation [tex]\((x-3)^2 + (y-9)^2 = 16\)[/tex], we need to recognize that this equation is in the standard form of a circle's equation, which is [tex]\((x-h)^2 + (y-k)^2 = r^2\)[/tex].
In the standard form equation [tex]\((x-h)^2 + (y-k)^2 = r^2\)[/tex]:
- [tex]\(h\)[/tex] and [tex]\(k\)[/tex] are the coordinates of the center of the circle [tex]\((h, k)\)[/tex].
- [tex]\(r^2\)[/tex] represents the square of the radius of the circle.
Comparing the given equation [tex]\((x-3)^2 + (y-9)^2 = 16\)[/tex] to the standard form, we can identify the following:
- The term [tex]\((x-3)\)[/tex] corresponds to [tex]\((x-h)\)[/tex], which means [tex]\(h = 3\)[/tex].
- The term [tex]\((y-9)\)[/tex] corresponds to [tex]\((y-k)\)[/tex], which means [tex]\(k = 9\)[/tex].
- The term [tex]\(16\)[/tex] corresponds to [tex]\(r^2\)[/tex], which means [tex]\(r = \sqrt{16} = 4\)[/tex]. However, the radius is not needed to determine the center.
Thus, the center of the circle [tex]\((h, k)\)[/tex] is [tex]\((3, 9)\)[/tex].
The correct choice is:
D. [tex]\((3, 9)\)[/tex]
In the standard form equation [tex]\((x-h)^2 + (y-k)^2 = r^2\)[/tex]:
- [tex]\(h\)[/tex] and [tex]\(k\)[/tex] are the coordinates of the center of the circle [tex]\((h, k)\)[/tex].
- [tex]\(r^2\)[/tex] represents the square of the radius of the circle.
Comparing the given equation [tex]\((x-3)^2 + (y-9)^2 = 16\)[/tex] to the standard form, we can identify the following:
- The term [tex]\((x-3)\)[/tex] corresponds to [tex]\((x-h)\)[/tex], which means [tex]\(h = 3\)[/tex].
- The term [tex]\((y-9)\)[/tex] corresponds to [tex]\((y-k)\)[/tex], which means [tex]\(k = 9\)[/tex].
- The term [tex]\(16\)[/tex] corresponds to [tex]\(r^2\)[/tex], which means [tex]\(r = \sqrt{16} = 4\)[/tex]. However, the radius is not needed to determine the center.
Thus, the center of the circle [tex]\((h, k)\)[/tex] is [tex]\((3, 9)\)[/tex].
The correct choice is:
D. [tex]\((3, 9)\)[/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.