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Which of the following points represents the center of a circle whose equation is [tex]\((x-3)^2+(y-6)^2=64\)[/tex]?

A. [tex]\((3,6)\)[/tex]

B. [tex]\((-3,6)\)[/tex]

C. [tex]\((-3,-6)\)[/tex]

D. [tex]\((3,-6)\)[/tex]

Sagot :

GinnyAnswer
To determine the center of the circle from its equation, let's first recall the standard form of a circle's equation:

[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]

In this equation, [tex]\((h, k)\)[/tex] represents the center of the circle and [tex]\(r\)[/tex] is the radius.

Given the equation of the circle:

[tex]\[ (x - 3)^2 + (y - 6)^2 = 64 \][/tex]

We can see that this equation matches the standard form, where:
- [tex]\(h = 3\)[/tex]
- [tex]\(k = 6\)[/tex]

Therefore, the center of the circle is the point:

[tex]\[ (3, 6) \][/tex]

So, the correct choice is:

A. [tex]\((3, 6)\)[/tex]
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