The standard form of the equation of a circle is

`(x-h)^2 + (y-k)^2 =r^2`

Fill in the values given for the center of the circle, h and k, as well as the radius given by r.

`(x-5)^2 + (y-7)^2 = 4^2`

`(x-5)^2 + (y-7)^2 =16`

`` Squaring an expression is the same as multiplying the expression by itself twice.

`(x-5)(x-5) +(y-7)^2 =16`

Use FOIL.

`(x^2 -10x+25) +(y-7)^2 =16`

`(x^2 -10x+25) + (y-7)(y-7) =16`

Use FOIL

`(x^2 -10x+25) + (y^2-14y+49) =16`

Combine like terms and reorder the polynomial.

`x^2-10x+y^2 -14y+74=16`

**The equation of the circle with center (5,7) and radius 4 is**

**x^2-10x+y^2-14y+74=16.**