onvert the given equation from standard to general form \[ (x-5)^{2}+(y-4)^{2}=36 \]

To convert the given equation from standard form to general form, we start with the standard form of a circle: \[ (x - 5)^2 + (y - 4)^2 = 36 \] We will expand the left side of the equation. 1. Expand \((x - 5)^2\): \[ (x - 5)^2 = x^2 - 10x + 25 \] 2. Expand \((y - 4)^2\): \[ (y - 4)^2 = y^2 - 8y + 16 \] 3. Substitute these expansions back into the equation: \[ x^2 - 10x + 25 + y^2 - 8y + 16 = 36 \] 4. Combine like terms: \[ x^2 + y^2 - 10x - 8y + 25 + 16 = 36 \] \[ x^2 + y^2 - 10x - 8y + 41 = 36 \] 5. Move 36 to the left side: \[ x^2 + y^2 - 10x - 8y + 41 - 36 = 0 \] \[ x^2 + y^2 - 10x - 8y + 5 = 0 \] Thus, the general form of the equation is: \[ x^2 + y^2 - 10x - 8y + 5 = 0 \]