A circle is drawn on a coordinate plane with the center point at (−8,−2) and a radius of 2. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point)

Question

Responses

(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
left parenthesis x minus 8 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 4

(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

Answer 1

To derive the equation of the circle in standard form, we start with the center of the circle and its radius. The general equation of a circle in standard form 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.

Given:

• Center: \((-8, -2)\)
• Radius: \(2\)

Here:

• \(h = -8\)
• \(k = -2\)
• \(r = 2\)

Now, substituting these values into the formula:

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

This simplifies to:

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

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

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