Final answer:
To transform the equation (x-2)²+(y-4)²=36 into the general equation of a circle, you expand and simplify to x² - 4x + y² - 8y - 16 = 0, which is in the form x²+y²+Dx+Ey+F=0.
Step-by-step explanation:
To transform the equation (x-2)²+(y-4)²=36 into the general equation of a circle, we start by expanding the squares and simplifying. The equation is already in the center-radius form of a circle, where the center is at (2, 4) and the radius is 6. However, the general equation of a circle has the form x²+y²+Dx+Ey+F=0, where D, E, and F are constants.
Let's expand the given equation:
- (x - 2)(x - 2) + (y - 4)(y - 4) = 36
- x² - 4x + 4 + y² - 8y + 16 = 36
Combine like terms and bring all terms to one side:
- x² - 4x + y² - 8y + 20 - 36 = 0
- x² - 4x + y² - 8y - 16 = 0
Now we have transformed the given equation into the general equation of a circle: x² - 4x + y² - 8y - 16 = 0.