Question

A circle is drawn on a coordinate plane with the center point at (−1,3)
(
−
1
,
3
)
and a radius of 5. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point)
Responses

(x−1)2+(y−3)2=25
(
𝑥
−
1
)
2
+
(
𝑦
−
3
)
2
=
25

left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 25

(x+3)2+(y−1)2=25
(
𝑥
+
3
)
2
+
(
𝑦
−
1
)
2
=
25

left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 25

(x−3)2+(y−1)2=25
(
𝑥
−
3
)
2
+
(
𝑦
−
1
)
2
=
25

left parenthesis x minus 3 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 25

(x+1)2+(y−3)2=25

Answer 1

Standard form: (x − h)^2 + (y − k)^2 = r^2. With center (h,k) = (−1,3) and r = 5:

(x − (−1))^2 + (y − 3)^2 = 5^2 → (x + 1)^2 + (y − 3)^2 = 25.

So the correct choice is (x+1)^2 + (y−3)^2 = 25.