Use the image to answer the question.

Question

A circle is plotted on a coordinate plane.

Which equation is the standard form of the equation of a circle drawn on the coordinate plane, derived from the Pythagorean Theorem?

(1 point)
Responses

(x−4)2+(y−3)2=25
left parenthesis x minus 4 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 25

x2+(y−5)2=25
x squared plus left parenthesis y minus 5 right parenthesis squared equals 25

x2+y2=25
x squared plus y squared equals 25

(x+4)2+(y+3)2=25
left parenthesis x plus 4 right parenthesis squared plus left parenthesis y plus 3 right parenthesis squared equals 25

Answer 1

The standard form of the equation of a circle is given by the equation \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.

Based on the options provided, we need to identify the equation that fits this form.

1. \((x−4)^2+(y−3)^2=25\) implies the center is at (4, 3) and the radius is \(r = 5\) (since \(25 = 5^2\)).
2. \(x^2+(y−5)^2=25\) implies the center is at (0, 5) and the radius is \(r = 5\).
3. \(x^2+y^2=25\) implies the center is at (0, 0) and the radius is \(r = 5\).
4. \((x+4)^2+(y+3)^2=25\) implies the center is at (-4, -3) and the radius is \(r = 5\).

Without the visual representation of the circle, I cannot determine which option is correct based solely on the given equations. However, all of these are valid standard forms of the equation of a circle.

If you have additional information about the center or radius of the circle in question, please provide it, and I can help determine which specific equation corresponds to that circle.