A circle is drawn on a coordinate plane with the center point at (5, 7) and a radius of 3. What is the equation of the circle?(1 point)

Question

Responses

(x − 7)2 + (y−5)2 = 3(x − 7)2 + (y−5)2 = 3

(x − 5)2 + (y−7)2 = 3(x − 5)2 + (y−7)2 = 3

(x − 7)2 + (y−5)2 = 9(x − 7)2 + (y−5)2 = 9

(x − 5)2 + (y−7)2 = 9(x − 5)2 + (y−7)2 = 9

Answer 1

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

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

In this case, the center of the circle is \((5, 7)\) and the radius is \(3\).

So, substituting \(h = 5\), \(k = 7\), and \(r = 3\) into the standard form gives:

\[ (x - 5)^2 + (y - 7)^2 = 3^2 \] \[ (x - 5)^2 + (y - 7)^2 = 9 \]

Thus, the correct equation of the circle is:

\[ \boxed{(x - 5)^2 + (y - 7)^2 = 9} \]