IDNLearn.com is the place where your questions are met with thoughtful and precise answers. Find the answers you need quickly and accurately with help from our knowledgeable and experienced experts.
Sagot :
To determine the center of the circle represented by the equation \((x + 9)^2 + (y - 6)^2 = 10^2\), we need to compare this equation to the standard form of a circle’s equation, which is:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
Here, \((h, k)\) represents the coordinates of the center of the circle, and \(r\) is the radius.
Given the equation in the problem:
[tex]\[ (x + 9)^2 + (y - 6)^2 = 10^2 \][/tex]
Let's rewrite \((x + 9)^2\) in a form that matches the standard equation format. Notice that:
[tex]\[ (x + 9) = (x - (-9)) \][/tex]
So, \((x + 9)^2\) can be written as:
[tex]\[ (x - (-9))^2 \][/tex]
Similarly, the term \((y - 6)^2\) already matches the standard form.
Now, comparing:
[tex]\[ (x - (-9))^2 + (y - 6)^2 = 10^2 \][/tex]
we see that \((h, k)\) corresponds to \((-9, 6)\).
Therefore, the center of the circle is:
[tex]\[ \boxed{(-9, 6)} \][/tex]
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
Here, \((h, k)\) represents the coordinates of the center of the circle, and \(r\) is the radius.
Given the equation in the problem:
[tex]\[ (x + 9)^2 + (y - 6)^2 = 10^2 \][/tex]
Let's rewrite \((x + 9)^2\) in a form that matches the standard equation format. Notice that:
[tex]\[ (x + 9) = (x - (-9)) \][/tex]
So, \((x + 9)^2\) can be written as:
[tex]\[ (x - (-9))^2 \][/tex]
Similarly, the term \((y - 6)^2\) already matches the standard form.
Now, comparing:
[tex]\[ (x - (-9))^2 + (y - 6)^2 = 10^2 \][/tex]
we see that \((h, k)\) corresponds to \((-9, 6)\).
Therefore, the center of the circle is:
[tex]\[ \boxed{(-9, 6)} \][/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.