Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation.
x^2+y^2+8x-2y-19=0

What is the equation of the circle in standard form?

Step 1 ：Given equation is \(x^2+y^2+8x-2y-19=0\).

Step 2 ：Rearrange the equation to group the x terms and y terms together: \(x^2+8x + y^2-2y = 19\).

Step 3 ：To complete the square, take half of the coefficient of x, square it, and add it to both sides. Do the same for y. The coefficient of x is 8, so half of it is 4, and \(4^2 = 16\). The coefficient of y is -2, so half of it is -1, and \((-1)^2 = 1\).

Step 4 ：Add 16 and 1 to both sides to get: \(x^2+8x+16 + y^2-2y+1 = 19+16+1\).

Step 5 ：Simplify to get: \((x+4)^2 + (y-1)^2 = 36\).

Step 6 ：\(\boxed{(x+4)^2 + (y-1)^2 = 36}\) is the equation of the circle in standard form.