IDNLearn.com offers a unique blend of expert answers and community insights. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.
Sagot :
To determine the equation of a circle with a given center and radius, we can use the standard form of the circle's equation:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.
Given:
- The center [tex]\(T(5, -1)\)[/tex] means [tex]\(h = 5\)[/tex] and [tex]\(k = -1\)[/tex].
- Radius [tex]\(r = 16\)[/tex].
Now, substitute the values of [tex]\(h\)[/tex], [tex]\(k\)[/tex], and [tex]\(r\)[/tex] into the standard form equation:
[tex]\[ (x - 5)^2 + (y + 1)^2 = 16^2 \][/tex]
Next, calculate [tex]\(16^2\)[/tex]:
[tex]\[ 16^2 = 256 \][/tex]
So the equation becomes:
[tex]\[ (x - 5)^2 + (y + 1)^2 = 256 \][/tex]
Given the options, we can see that this matches option B:
B. [tex]\((x - 5)^2 + (y + 1)^2 = 256\)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.
Given:
- The center [tex]\(T(5, -1)\)[/tex] means [tex]\(h = 5\)[/tex] and [tex]\(k = -1\)[/tex].
- Radius [tex]\(r = 16\)[/tex].
Now, substitute the values of [tex]\(h\)[/tex], [tex]\(k\)[/tex], and [tex]\(r\)[/tex] into the standard form equation:
[tex]\[ (x - 5)^2 + (y + 1)^2 = 16^2 \][/tex]
Next, calculate [tex]\(16^2\)[/tex]:
[tex]\[ 16^2 = 256 \][/tex]
So the equation becomes:
[tex]\[ (x - 5)^2 + (y + 1)^2 = 256 \][/tex]
Given the options, we can see that this matches option B:
B. [tex]\((x - 5)^2 + (y + 1)^2 = 256\)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.