Question

A circle is drawn on a coordinate plane with the center point at (−2,0) and a radius of 7. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point)
Responses

x2+(y−2)2=49
x squared plus left parenthesis y minus 2 right parenthesis squared equals 49

x2+(y+2)2=49
x squared plus left parenthesis y plus 2 right parenthesis squared equals 49

(x−2)2+y2=49
left parenthesis x minus 2 right parenthesis squared plus y squared equals 49

(x+2)2+y2=49

Answer 1

To derive the equation of the circle in standard form, we can use the general formula for a circle's equation in the coordinate plane, which 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:
- The center of the circle is \((-2, 0)\), so \(h = -2\) and \(k = 0\).
- The radius \(r = 7\).

Now we can plug these values into the formula:

1. Substitute \(h\) and \(k\):
\[
(x - (-2))^2 + (y - 0)^2 = 7^2
\]

2. Simplifying this gives:
\[
(x + 2)^2 + y^2 = 49
\]

So the equation of the circle in standard form is:

\[
(x + 2)^2 + y^2 = 49
\]

From the provided options, the correct one is:
\((x + 2)^2 + y^2 = 49\).