1. Problem: Find the center and radius of a circle given by the equation $$x^2 + y^2 - 6x + 8y + 9 = 0$$. 2. Formula: The general form of a circle is $$x^2 + y^2 + Dx + Ey + F = 0$$. 3. To find the center and radius, complete the square for both $x$ and $y$ terms. 4. Rewrite the equation grouping $x$ and $y$ terms: $$x^2 - 6x + y^2 + 8y = -9$$. 5. Complete the square: - For $x$: $$x^2 - 6x = (x - 3)^2 - 9$$ - For $y$: $$y^2 + 8y = (y + 4)^2 - 16$$ 6. Substitute back: $$ (x - 3)^2 - 9 + (y + 4)^2 - 16 = -9 $$ 7. Simplify: $$ (x - 3)^2 + (y + 4)^2 - 25 = -9 $$ 8. Add 25 to both sides: $$ (x - 3)^2 + (y + 4)^2 = 16 $$ 9. The center is at $$ (3, -4) $$ and the radius is $$ \sqrt{16} = 4 $$. This method applies to all circle equations in general form. [Note: Only the first problem is solved as per instructions.]