Question

Question
Use the image to answer the 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 plus 4 right parenthesis squared plus left parenthesis y plus 3 right parenthesis squared equals 25

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

(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+y2=25

Answer 1

The standard form of the equation of a circle 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.

Based on the options provided, the equation that follows this standard form is:

\[
(x + 4)^2 + (y + 3)^2 = 25
\]

Here, the center of the circle is at \((-4, -3)\) and the radius is \(5\) (since \(25 = 5^2\)).

Therefore, the correct response is:

\((x+4)² + (y+3)² = 25\)