The standard form of the equation of a circle in the coordinate plane is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Among the provided options, the equations that fit this format are:
- \((x + 4)^2 + (y + 3)^2 = 25\), which has a center at \((-4, -3)\) and a radius of \(5\).
- \((x - 4)^2 + (y - 3)^2 = 25\), which has a center at \((4, 3)\) and a radius of \(5\).
- \(x^2 + (y - 5)^2 = 25\), which is equivalent to \((x - 0)^2 + (y - 5)^2 = 25\), making it a circle centered at \((0, 5)\) with a radius of \(5\).
The first two options are more explicit in showing the center, while the last option can be interpreted as a circle whose center is at the origin in the x-direction.
Thus, all three, except the first option, meet the standard form of the equation of a circle based on the structure provided.
If you are looking for the equation that visually indicates a traditional circle equation most commonly derived from Pythagorean theorem, the two forms with transformations are the standard form; hence the most suitable answers would be:
- \((x + 4)^2 + (y + 3)^2 = 25\)
- \((x - 4)^2 + (y - 3)^2 = 25\)
Choose either of those as they are standard forms of a circle's equation.