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

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

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

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

x2+(y+2)2=49

Answer 1

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

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

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

Given:

• Center: \((-2, 0)\), so \(h = -2\) and \(k = 0\)
• Radius: \(7\), so \(r = 7\)

Now, we substitute the values into the formula:

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

This simplifies to:

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

Thus, the equation of the circle in standard form is:

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

Therefore, the correct response is:

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