Write the standard form of the equation of the circle with the given center and radius. Center \( (2,5), r=7 \)

The equation of a circle in standard form 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. For the center \( (2, 5) \) and radius \( 7 \), we substitute these values into the formula. Thus, the equation becomes \( (x - 2)^2 + (y - 5)^2 = 7^2 \), which simplifies to \( (x - 2)^2 + (y - 5)^2 = 49 \). Now you've got the circle all set up! Just imagine drawing that circle on a graph; it would swirl around the center point (2, 5) and extend outward in every direction to 7 units away. The equation of the circle captures that perfect round shape!