Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To find the center and the radius of the circle given by the equation [tex]\((x + 2)^2 + (y - 5)^2 = 49\)[/tex], we can follow these steps:
1. Identify the standard form of the circle's equation: The standard form of a circle's equation is [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex], where [tex]\((h, k)\)[/tex] represents the center of the circle, and [tex]\(r\)[/tex] is the radius.
2. Compare the given equation to the standard form:
- The given equation is [tex]\((x + 2)^2 + (y - 5)^2 = 49\)[/tex].
- Here, [tex]\((x + 2)^2\)[/tex] can be rewritten as [tex]\((x - (-2))^2\)[/tex], thus identifying [tex]\(h = -2\)[/tex].
- Similarly, [tex]\((y - 5)^2\)[/tex] is already in the required form with [tex]\(k = 5\)[/tex].
3. Determine the values of [tex]\(h\)[/tex] and [tex]\(k\)[/tex]:
- From the comparison, we find that [tex]\(h = -2\)[/tex] and [tex]\(k = 5\)[/tex].
4. Find the radius: The right side of the equation represents [tex]\(r^2\)[/tex]:
- We have [tex]\(r^2 = 49\)[/tex].
- To find the radius [tex]\(r\)[/tex], take the square root of 49:
[tex]\[ r = \sqrt{49} = 7 \][/tex]
So, the circle's center has coordinates [tex]\((-2, 5)\)[/tex], and the radius is [tex]\(7\)[/tex] units long.
Therefore, the completed information is:
- Center coordinates: [tex]\((-2, 5)\)[/tex]
- Radius: [tex]\(7\)[/tex] units long
1. Identify the standard form of the circle's equation: The standard form of a circle's equation is [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex], where [tex]\((h, k)\)[/tex] represents the center of the circle, and [tex]\(r\)[/tex] is the radius.
2. Compare the given equation to the standard form:
- The given equation is [tex]\((x + 2)^2 + (y - 5)^2 = 49\)[/tex].
- Here, [tex]\((x + 2)^2\)[/tex] can be rewritten as [tex]\((x - (-2))^2\)[/tex], thus identifying [tex]\(h = -2\)[/tex].
- Similarly, [tex]\((y - 5)^2\)[/tex] is already in the required form with [tex]\(k = 5\)[/tex].
3. Determine the values of [tex]\(h\)[/tex] and [tex]\(k\)[/tex]:
- From the comparison, we find that [tex]\(h = -2\)[/tex] and [tex]\(k = 5\)[/tex].
4. Find the radius: The right side of the equation represents [tex]\(r^2\)[/tex]:
- We have [tex]\(r^2 = 49\)[/tex].
- To find the radius [tex]\(r\)[/tex], take the square root of 49:
[tex]\[ r = \sqrt{49} = 7 \][/tex]
So, the circle's center has coordinates [tex]\((-2, 5)\)[/tex], and the radius is [tex]\(7\)[/tex] units long.
Therefore, the completed information is:
- Center coordinates: [tex]\((-2, 5)\)[/tex]
- Radius: [tex]\(7\)[/tex] units long
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.