write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k)

r=10; (h,k)=(8,-6)

Given: C(h,k) = C(8,-6), r = 10.

STD Form: (x-h)^2 + (y-k)^2 = r^2.
(x-8)^2 + (y+6)^2 = 100.

x^2-16x+64 + y^2+12y+36-100 = 0.
X^2 + Y^2 -16x + 12y - 64 = 0
Gen. Form: X^2 + Y^2 Ax + By + C = 0.

To write the standard form and general form equations of a circle, we can use the formula:

Standard Form Equation: (x - h)^2 + (y - k)^2 = r^2
General Form Equation: x^2 + y^2 + Dx + Ey + F = 0

Given: r = 10, (h, k) = (8, -6)

1. Standard Form Equation:
Substitute the values of r, h, and k into the standard form equation formula:
(x - 8)^2 + (y - (-6))^2 = 10^2

Simplify:
(x - 8)^2 + (y + 6)^2 = 100

This is the standard form equation of the circle.

2. General Form Equation:
Expand the equation further:
(x^2 - 16x + 64) + (y^2 + 12y + 36) = 100

Rearrange the terms:
x^2 + y^2 - 16x + 12y + 64 + 36 - 100 = 0

Simplify:
x^2 + y^2 - 16x + 12y = 0

This is the general form equation of the circle.

Thus, the standard form equation of the circle is (x - 8)^2 + (y + 6)^2 = 100, and the general form equation is x^2 + y^2 - 16x + 12y = 0.