Question

page 8 of 8 Equation of a Circle Quick Check 2 of 52 of 5 Items Question 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) 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−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+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+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 Skip to navigation

Answer 1

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

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

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

Given that the center of the circle is at \((-8, -2)\) and the radius is \(2\), we can substitute these values into the formula:

1. Identify \(h\) and \(k\):

   • \(h = -8\)
   • \(k = -2\)

2. Calculate \(r^2\):

   • \(r = 2\)
   • \(r^2 = 2^2 = 4\)

Now we can write the equation:

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

This simplifies to:

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

Thus, the correct answer from the provided options is:

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