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)

Question

Responses

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

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

Answer 1

The standard form of a circle's equation 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.

In this case, the center is \((-2, 0)\) and the radius is \(7\). So, we substitute \(h = -2\), \(k = 0\), and \(r = 7\) into the equation:

\[ (x - (-2))^2 + (y - 0)^2 = 7^2 \]

This simplifies to:

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

Therefore, the correct equation of the circle in standard form is:

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

The correct response is:

\((x+2)^2 + y^2 = 49\) (which is the third option).