A circle is plotted on a coordinate plane.

Question

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−6)2+(y−2)2=16
left parenthesis x minus 6 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 16

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

(x−2)2+(y+2)2=16
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y plus 2 right parenthesis squared equals 16

(x+2)2+(y−6)2=4

Answer 1

The standard form of the equation of a circle is given by the formula:

\[ (x - h)^2 + (y - k)^2 = r^2 \]

where \((h, k)\) is the center of the circle and \(r\) is the radius.

Let's analyze the options:

1. \((x−6)^2 + (y−2)^2 = 16\)

   • Center: (6, 2), Radius: 4 (since \(r^2 = 16\))

2. \((x−2)^2 + (y−2)^2 = 4\)

   • Center: (2, 2), Radius: 2 (since \(r^2 = 4\))

3. \((x−2)^2 + (y+2)^2 = 16\)

   • Center: (2, -2), Radius: 4 (since \(r^2 = 16\))

4. \((x+2)^2 + (y−6)^2 = 4\)

   • Center: (-2, 6), Radius: 2 (since \(r^2 = 4\))

Any of these equations can represent a circle. However, since you are looking for the standard form derived from the Pythagorean Theorem, all of these fit the form, but one common example is having a clear integer center and radius.

If you specifically want to see one clear example in standard form, the first option is the most comprehensive:

\((x - 6)^2 + (y - 2)^2 = 16\)

So, the answer would be the first option:

\((x−6)^2 + (y−2)^2 = 16\)