Question
The center of the circle is (5,5) for the following circle.
x^2+y^2=25
Question 9 options:
True
False
x^2+y^2=25
Question 9 options:
True
False
Answers
GPT-4o mini
To determine whether the statement is true or false, we need to rewrite the equation of the circle \( x^2 + y^2 = 25 \) in standard form.
The standard equation for a circle is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center and \(r\) is the radius of the circle.
From the given equation:
\[
x^2 + y^2 = 25
\]
we can see that it is equivalent to:
\[
(x - 0)^2 + (y - 0)^2 = 5^2
\]
This indicates that the center of the circle is at \((0, 0)\) and the radius is \(5\).
So, the center of the circle is \((0, 0)\), not \((5, 5)\).
Thus, the statement is **False**.
The standard equation for a circle is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center and \(r\) is the radius of the circle.
From the given equation:
\[
x^2 + y^2 = 25
\]
we can see that it is equivalent to:
\[
(x - 0)^2 + (y - 0)^2 = 5^2
\]
This indicates that the center of the circle is at \((0, 0)\) and the radius is \(5\).
So, the center of the circle is \((0, 0)\), not \((5, 5)\).
Thus, the statement is **False**.