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Which equation represents a circle with a center at [tex]\((-5,5)\)[/tex] and a radius of 3 units?

A. [tex]\((x+5)^2+(y-5)^2=9\)[/tex]

B. [tex]\((x-5)^2+(y+5)^2=9\)[/tex]

C. [tex]\((x+5)^2+(y-5)^2=3\)[/tex]

D. [tex]\((x-5)^2+(y+5)^2=3\)[/tex]

Sagot :

GinnyAnswer
To find the equation of a circle, we use the general form of a circle's equation:

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

Where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.

Given the center [tex]\((-5, 5)\)[/tex]:
- [tex]\(h = -5\)[/tex]
- [tex]\(k = 5\)[/tex]

And the radius [tex]\(r = 3\)[/tex].

Now, we substitute these values into the general form:

[tex]$(x - (-5))^2 + (y - 5)^2 = 3^2$[/tex]

Simplify the expression inside the parentheses:

[tex]$(x + 5)^2 + (y - 5)^2 = 9$[/tex]

So, the equation of the circle is:

[tex]$(x + 5)^2 + (y - 5)^2 = 9$[/tex]

Therefore, the correct answer is:
A. [tex]$(x+5)^2+(y-5)^2=9$[/tex]
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