A circle is drawn on a coordinate plane with the center point at (−2,0)

Question

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 plus 2 right parenthesis squared plus y squared equals 49

(x−2)2+y2=49

Answer 1

The standard form of the equation of a circle with center at \((h, k)\) and radius \(r\) is given by the formula:

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

In this case, the center is \((-2, 0)\) and the radius is \(7\). So, we have:

• \(h = -2\)
• \(k = 0\)
• \(r = 7\)

Now substituting these values into the standard form equation:

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

This simplifies to:

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

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

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