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

Question

UpStudy AI · Accepted Answer

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:

$$
x^2 + y^2 - 10x - 8y + 5 = 0
$$
The general form of the equation is $$ x^2 + y^2 - 10x - 8y + 5 = 0 $$.

onvert the given equation from standard to general form