Question

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

Answer 1

Equation: (x + 8)^2 + (y + 2)^2 = 4.

Reason: For center (h,k)=(-8,-2) and radius r=2, distance formula gives sqrt((x+8)^2+(y+2)^2)=2. Squaring both sides yields (x+8)^2+(y+2)^2=4.