Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

If the equation of a circle is [tex]$(x+5)^2+(y-7)^2=36$[/tex], its center point is:

A. [tex]$(5, -7)$[/tex]
B. [tex]$(5, 7)$[/tex]
C. [tex]$(-5, 7)$[/tex]

Sagot :

GinnyAnswer
To find the center of the circle given by the equation \((x+5)^2 + (y-7)^2 = 36\), we need to identify 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 center of the circle and \(r\) represents the radius.

In the given equation:
[tex]\[ (x+5)^2 + (y-7)^2 = 36 \][/tex]

we should match it to the standard form. Comparing the two equations, we observe that:

- \( (x-h)^2 \) matches with \((x+5)^2\), which indicates that \( h = -5 \). This is because \((x - (-5)) = (x + 5)\).

- \( (y-k)^2 \) matches with \((y-7)^2\), which indicates that \( k = 7 \).

Therefore, the center \((h, k)\) of the circle is:

[tex]\[ (-5, 7) \][/tex]

So, the center point of the circle is [tex]\(\boxed{(-5, 7)}\)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.