A circle is drawn on a coordinate plane with the center point at (−8,−2)

Question

and a radius of 2. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point)
Responses

(x−2)2+(y−8)2=2
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 8 right parenthesis squared equals 2

(x+2)2+(y+8)2=2
left parenthesis x plus 2 right parenthesis squared plus left parenthesis y plus 8 right parenthesis squared equals 2

(x+8)2+(y+2)2=4
left parenthesis x plus 8 right parenthesis squared plus left parenthesis y plus 2 right parenthesis squared equals 4

(x−8)2+(y−2)2=4

Answer 1

To derive the equation of the circle in standard form, we use the following formula for the equation of a circle:

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

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

Given:

• Center \((h, k) = (-8, -2)\)
• Radius \(r = 2\)

1. Substitute the values of \(h\), \(k\), and \(r\) into the formula:

\[ (x - (-8))^2 + (y - (-2))^2 = 2^2 \]

2. Simplify this:

\[ (x + 8)^2 + (y + 2)^2 = 4 \]

Thus, the equation of the circle in standard form is:

\[ \boxed{(x + 8)^2 + (y + 2)^2 = 4} \]

This corresponds to the response: \((x+8)^2+(y+2)^2=4\).