IDNLearn.com: Your reliable source for finding expert answers. Get accurate and timely answers to your queries from our extensive network of experienced professionals.
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]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.